Patience, young “Padovan”Output the van der Corput sequenceGenerate n-ary numbersGenerate a Padovan SpiralGenerate an ASCII Padovan SpiralGolf a Custom Fibonacci SequenceImplement the Fibonacci sequence… Shifted to the rightDizzy integer enumerationModulus SummationFour Spiraling AxesIt's getting harder and harder to be composite these days
Can I make popcorn with any corn?
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Patience, young “Padovan”
Output the van der Corput sequenceGenerate n-ary numbersGenerate a Padovan SpiralGenerate an ASCII Padovan SpiralGolf a Custom Fibonacci SequenceImplement the Fibonacci sequence… Shifted to the rightDizzy integer enumerationModulus SummationFour Spiraling AxesIt's getting harder and harder to be composite these days
$begingroup$
Everyone knows the Fibonacci sequence:
You take a square, attach an equal square to it, then repeatedly attach a square whose side length is equal to the largest side length of the resulting rectangle.
The result is a beautiful spiral of squares whose sequence of numbers is the Fibonacci sequence:
But, what if we didn't want to use squares?
If we use equilateral triangles—instead of squares—in a similar fashion, we get an equally beautiful spiral of triangles and a new sequence: the Padovan sequence, aka A000931:
Task:
Given a positive integer, $N$, output $a_N$, the $N$th term in the Padovan sequence OR the first $N$ terms.
Assume that the first three terms of the sequence are all $1$. Thus, the sequence will start as follows:
$$
1,1,1,2,2,3,...
$$
Input:
Any positive integer $Nge0$
Invalid input does not have to be taken into account
Output:
The $N$th term in the Padovan sequence OR the first $N$ terms of the Padovan sequence.
If the first $N$ terms are printed out, the output can be whatever is convenient (list/array, multi-line string, etc.)
Can be either $0$-indexed or $1$-indexed
Test Cases:
(0-indexed, $N$th term)
Input | Output
--------------
0 | 1
1 | 1
2 | 1
4 | 2
6 | 4
14 | 37
20 | 200
33 | 7739
(0-indexed, first $N$ terms)
Input | Output
--------------
1 | 1
3 | 1,1,1
4 | 1,1,1,2
7 | 1,1,1,2,2,3,4
10 | 1,1,1,2,2,3,4,5,7,9
12 | 1,1,1,2,2,3,4,5,7,9,12,16
Rules:
This is code-golf: the fewer bytes, the better!
Standard loopholes are forbidden.
code-golf number sequence
asked 1 hour ago
TauTau
786313
$endgroup$
add a comment |
$begingroup$
Everyone knows the Fibonacci sequence:
You take a square, attach an equal square to it, then repeatedly attach a square whose side length is equal to the largest side length of the resulting rectangle.
The result is a beautiful spiral of squares whose sequence of numbers is the Fibonacci sequence:
But, what if we didn't want to use squares?
If we use equilateral triangles—instead of squares—in a similar fashion, we get an equally beautiful spiral of triangles and a new sequence: the Padovan sequence, aka A000931:
Task:
Given a positive integer, $N$, output $a_N$, the $N$th term in the Padovan sequence OR the first $N$ terms.
Assume that the first three terms of the sequence are all $1$. Thus, the sequence will start as follows:
$$
1,1,1,2,2,3,...
$$
Input:
Any positive integer $Nge0$
Invalid input does not have to be taken into account
Output:
The $N$th term in the Padovan sequence OR the first $N$ terms of the Padovan sequence.
If the first $N$ terms are printed out, the output can be whatever is convenient (list/array, multi-line string, etc.)
Can be either $0$-indexed or $1$-indexed
Test Cases:
(0-indexed, $N$th term)
Input | Output
--------------
0 | 1
1 | 1
2 | 1
4 | 2
6 | 4
14 | 37
20 | 200
33 | 7739
(0-indexed, first $N$ terms)
Input | Output
--------------
1 | 1
3 | 1,1,1
4 | 1,1,1,2
7 | 1,1,1,2,2,3,4
10 | 1,1,1,2,2,3,4,5,7,9
12 | 1,1,1,2,2,3,4,5,7,9,12,16
Rules:
This is code-golf: the fewer bytes, the better!
Standard loopholes are forbidden.
code-golf number sequence
asked 1 hour ago
TauTau
786313
$endgroup$
$begingroup$
Sandbox post can be found here.
$endgroup$
– Tau
1 hour ago
1
$begingroup$
14(0-indexed) is shown as outputting28while I believe it should yield37
$endgroup$
– Jonathan Allan
45 mins ago
$begingroup$
@JonathanAllan yes, you are correct. I fixed the last two test cases for $N$th term but not that one. The post has been edited.
$endgroup$
– Tau
43 mins ago
add a comment |
$begingroup$
Everyone knows the Fibonacci sequence:
You take a square, attach an equal square to it, then repeatedly attach a square whose side length is equal to the largest side length of the resulting rectangle.
The result is a beautiful spiral of squares whose sequence of numbers is the Fibonacci sequence:
But, what if we didn't want to use squares?
If we use equilateral triangles—instead of squares—in a similar fashion, we get an equally beautiful spiral of triangles and a new sequence: the Padovan sequence, aka A000931:
Task:
Given a positive integer, $N$, output $a_N$, the $N$th term in the Padovan sequence OR the first $N$ terms.
Assume that the first three terms of the sequence are all $1$. Thus, the sequence will start as follows:
$$
1,1,1,2,2,3,...
$$
Input:
Any positive integer $Nge0$
Invalid input does not have to be taken into account
Output:
The $N$th term in the Padovan sequence OR the first $N$ terms of the Padovan sequence.
If the first $N$ terms are printed out, the output can be whatever is convenient (list/array, multi-line string, etc.)
Can be either $0$-indexed or $1$-indexed
Test Cases:
(0-indexed, $N$th term)
Input | Output
--------------
0 | 1
1 | 1
2 | 1
4 | 2
6 | 4
14 | 37
20 | 200
33 | 7739
(0-indexed, first $N$ terms)
Input | Output
--------------
1 | 1
3 | 1,1,1
4 | 1,1,1,2
7 | 1,1,1,2,2,3,4
10 | 1,1,1,2,2,3,4,5,7,9
12 | 1,1,1,2,2,3,4,5,7,9,12,16
Rules:
This is code-golf: the fewer bytes, the better!
Standard loopholes are forbidden.
code-golf number sequence
asked 1 hour ago
TauTau
786313
$endgroup$
Everyone knows the Fibonacci sequence:
You take a square, attach an equal square to it, then repeatedly attach a square whose side length is equal to the largest side length of the resulting rectangle.
The result is a beautiful spiral of squares whose sequence of numbers is the Fibonacci sequence:
But, what if we didn't want to use squares?
If we use equilateral triangles—instead of squares—in a similar fashion, we get an equally beautiful spiral of triangles and a new sequence: the Padovan sequence, aka A000931:
Task:
Given a positive integer, $N$, output $a_N$, the $N$th term in the Padovan sequence OR the first $N$ terms.
Assume that the first three terms of the sequence are all $1$. Thus, the sequence will start as follows:
$$
1,1,1,2,2,3,...
$$
Input:
Any positive integer $Nge0$
Invalid input does not have to be taken into account
Output:
The $N$th term in the Padovan sequence OR the first $N$ terms of the Padovan sequence.
If the first $N$ terms are printed out, the output can be whatever is convenient (list/array, multi-line string, etc.)
Can be either $0$-indexed or $1$-indexed
Test Cases:
(0-indexed, $N$th term)
Input | Output
--------------
0 | 1
1 | 1
2 | 1
4 | 2
6 | 4
14 | 37
20 | 200
33 | 7739
(0-indexed, first $N$ terms)
Input | Output
--------------
1 | 1
3 | 1,1,1
4 | 1,1,1,2
7 | 1,1,1,2,2,3,4
10 | 1,1,1,2,2,3,4,5,7,9
12 | 1,1,1,2,2,3,4,5,7,9,12,16
Rules:
This is code-golf: the fewer bytes, the better!
Standard loopholes are forbidden.
code-golf number sequence
code-golf number sequence
asked 1 hour ago
TauTau
786313
asked 1 hour ago
TauTau
786313
edited 42 mins ago
Tau
asked 1 hour ago
TauTau
786313
asked 1 hour ago
TauTau
786313
asked 1 hour ago
TauTau
786313
786313
$begingroup$
Sandbox post can be found here.
$endgroup$
– Tau
1 hour ago
1
$begingroup$
14(0-indexed) is shown as outputting28while I believe it should yield37
$endgroup$
– Jonathan Allan
45 mins ago
$begingroup$
@JonathanAllan yes, you are correct. I fixed the last two test cases for $N$th term but not that one. The post has been edited.
$endgroup$
– Tau
43 mins ago
add a comment |
$begingroup$
Sandbox post can be found here.
$endgroup$
– Tau
1 hour ago
1
$begingroup$
14(0-indexed) is shown as outputting28while I believe it should yield37
$endgroup$
– Jonathan Allan
45 mins ago
$begingroup$
@JonathanAllan yes, you are correct. I fixed the last two test cases for $N$th term but not that one. The post has been edited.
$endgroup$
– Tau
43 mins ago
$begingroup$
Sandbox post can be found here.
$endgroup$
– Tau
1 hour ago
$begingroup$
Sandbox post can be found here.
$endgroup$
– Tau
1 hour ago
1
1
$begingroup$
14 (0-indexed) is shown as outputting 28 while I believe it should yield 37$endgroup$
– Jonathan Allan
45 mins ago
$begingroup$
14 (0-indexed) is shown as outputting 28 while I believe it should yield 37$endgroup$
– Jonathan Allan
45 mins ago
$begingroup$
@JonathanAllan yes, you are correct. I fixed the last two test cases for $N$th term but not that one. The post has been edited.
$endgroup$
– Tau
43 mins ago
$begingroup$
@JonathanAllan yes, you are correct. I fixed the last two test cases for $N$th term but not that one. The post has been edited.
$endgroup$
– Tau
43 mins ago
add a comment |
12 Answers
12
active
oldest
votes
$begingroup$
Python 2, 30 bytes
f=lambda n:n<3or f(n-2)+f(n-3)
Try it online!
Returns the n'th term zero indexed. Outputs True for 1.
answered 51 mins ago
xnorxnor
93.3k18190448
$endgroup$
add a comment |
$begingroup$
Oasis, 5 bytes
nth term 0-indexed
cd+1V
Try it online!
Explanation
1V # a(0) = 1
# a(1) = 1
# a(2) = 1
# a(n) =
c # a(n-2)
+ # +
d # a(n-3)
answered 1 hour ago
EmignaEmigna
47.4k433144
$endgroup$
add a comment |
$begingroup$
Wolfram Language (Mathematica), 33 bytes
a@0=a@1=a@2=1;a@n_:=a[n-2]+a[n-3]
1-indexed, returns the nth term
Try it online!
answered 1 hour ago
J42161217J42161217
13.8k21253
$endgroup$
add a comment |
$begingroup$
Python 2, 56 48 bytes
f=lambda n,a=1,b=1,c=1:n>2and f(n-1,b,c,a+b)or c
Try it online!
Returns nth value, 0-indexed.
answered 54 mins ago
Chas BrownChas Brown
5,2091523
$endgroup$
add a comment |
$begingroup$
J, 26 bytes
0.5<.@+1.04535%~1.32472^<:
Try it online!
Uses the closed form formula.
answered 55 mins ago
JonahJonah
2,5911017
$endgroup$
add a comment |
$begingroup$
Jelly, 11 bytes
5B+Ɲ2ị;Ʋ⁸¡Ḣ
Try it online!
0-indexed.
answered 40 mins ago
Erik the OutgolferErik the Outgolfer
33k429106
$endgroup$
$begingroup$
Can you specify whether this answer is 0-indexed or 1-indexed?
$endgroup$
– Tau
37 mins ago
$begingroup$
@Tau It's 0-indexed. I've edited it in.
$endgroup$
– Erik the Outgolfer
36 mins ago
add a comment |
$begingroup$
Jelly, 10 bytes
‘HŻcḤạ¥¥‘S
A monadic Link accepting n (1-indexed) which yields P(n).
Try it online!
answered 34 mins ago
Jonathan AllanJonathan Allan
53.7k535173
$endgroup$
add a comment |
$begingroup$
Haskell, 26 bytes
(l!!)
l=1:1:1:2:scanl(+)2l
Try it online! Outputs the n'th term zero-indexed.
I thought that the "obvious" recursive solution below would be unbeatable, but then I found this. It's similar to the classic golfy expression l=1:scanl(+)1l for the infinite Fibonacci list, but here the difference between adjacent elements is the term 4 positions back. We can more directly write l=1:1:zipWith(+)l(0:l), but that's longer.
If this challenge allowed infinite list output, we could cut the first line and have 20 bytes.
27 bytes
f n|n<3=1|1>0=f(n-2)+f(n-3)
Try it online!
answered 2 mins ago
xnorxnor
93.3k18190448
$endgroup$
add a comment |
$begingroup$
C# (Visual C# Interactive Compiler), 34 bytes
int f(int g)=>g<3?1:f(g-2)+f(g-3);
Try it online!
answered 21 mins ago
Embodiment of IgnoranceEmbodiment of Ignorance
2,808127
$endgroup$
add a comment |
$begingroup$
JavaScript (ES6), 23 bytes
Implements the recursive definition of A000931. Returns the $N$th term, 0-indexed.
f=n=>n<3||f(n-2)+f(n-3)
Try it online!
answered 20 mins ago
ArnauldArnauld
80.5k797333
$endgroup$
add a comment |
$begingroup$
Japt -N, 12 bytes
<3ªßUµ2 +ß´U
Try it
answered 11 mins ago
Embodiment of IgnoranceEmbodiment of Ignorance
2,808127
$endgroup$
add a comment |
$begingroup$
Retina, 47 42 bytes
K`0¶1¶0
"$+"+`.+¶(.+)¶.+$
$&¶$.(*_$1*
6,G`
Try it online! Outputs the first n terms on separate lines. Explanation:
K`0¶1¶0
Replace the input with the terms for -2, -1 and 0.
"$+"+`.+¶(.+)¶.+$
$&¶$.(*_$1*
Generate the next n terms using the recurrence relation. *_ here is short for $&*_ which converts the (first) number in the match to unary, while $1* is short for $1*_ which converts the middle number to unary. The $.( returns the decimal sum of its unary arguments, i.e. the sum of the first and middle numbers.
6,G`
Discard the first six characters, i.e. the first three lines.
answered 11 mins ago
NeilNeil
82.6k745179
$endgroup$
add a comment |
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12 Answers
12
active
oldest
votes
12 Answers
12
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Python 2, 30 bytes
f=lambda n:n<3or f(n-2)+f(n-3)
Try it online!
Returns the n'th term zero indexed. Outputs True for 1.
answered 51 mins ago
xnorxnor
93.3k18190448
$endgroup$
add a comment |
$begingroup$
Python 2, 30 bytes
f=lambda n:n<3or f(n-2)+f(n-3)
Try it online!
Returns the n'th term zero indexed. Outputs True for 1.
answered 51 mins ago
xnorxnor
93.3k18190448
$endgroup$
add a comment |
$begingroup$
Python 2, 30 bytes
f=lambda n:n<3or f(n-2)+f(n-3)
Try it online!
Returns the n'th term zero indexed. Outputs True for 1.
answered 51 mins ago
xnorxnor
93.3k18190448
$endgroup$
Python 2, 30 bytes
f=lambda n:n<3or f(n-2)+f(n-3)
Try it online!
Returns the n'th term zero indexed. Outputs True for 1.
answered 51 mins ago
xnorxnor
93.3k18190448
edited 36 mins ago
answered 51 mins ago
xnorxnor
93.3k18190448
answered 51 mins ago
xnorxnor
93.3k18190448
answered 51 mins ago
xnorxnor
93.3k18190448
93.3k18190448
add a comment |
add a comment |
$begingroup$
Oasis, 5 bytes
nth term 0-indexed
cd+1V
Try it online!
Explanation
1V # a(0) = 1
# a(1) = 1
# a(2) = 1
# a(n) =
c # a(n-2)
+ # +
d # a(n-3)
answered 1 hour ago
EmignaEmigna
47.4k433144
$endgroup$
add a comment |
$begingroup$
Oasis, 5 bytes
nth term 0-indexed
cd+1V
Try it online!
Explanation
1V # a(0) = 1
# a(1) = 1
# a(2) = 1
# a(n) =
c # a(n-2)
+ # +
d # a(n-3)
answered 1 hour ago
EmignaEmigna
47.4k433144
$endgroup$
add a comment |
$begingroup$
Oasis, 5 bytes
nth term 0-indexed
cd+1V
Try it online!
Explanation
1V # a(0) = 1
# a(1) = 1
# a(2) = 1
# a(n) =
c # a(n-2)
+ # +
d # a(n-3)
answered 1 hour ago
EmignaEmigna
47.4k433144
$endgroup$
Oasis, 5 bytes
nth term 0-indexed
cd+1V
Try it online!
Explanation
1V # a(0) = 1
# a(1) = 1
# a(2) = 1
# a(n) =
c # a(n-2)
+ # +
d # a(n-3)
answered 1 hour ago
EmignaEmigna
47.4k433144
answered 1 hour ago
EmignaEmigna
47.4k433144
answered 1 hour ago
EmignaEmigna
47.4k433144
answered 1 hour ago
EmignaEmigna
47.4k433144
47.4k433144
add a comment |
add a comment |
$begingroup$
Wolfram Language (Mathematica), 33 bytes
a@0=a@1=a@2=1;a@n_:=a[n-2]+a[n-3]
1-indexed, returns the nth term
Try it online!
answered 1 hour ago
J42161217J42161217
13.8k21253
$endgroup$
add a comment |
$begingroup$
Wolfram Language (Mathematica), 33 bytes
a@0=a@1=a@2=1;a@n_:=a[n-2]+a[n-3]
1-indexed, returns the nth term
Try it online!
answered 1 hour ago
J42161217J42161217
13.8k21253
$endgroup$
add a comment |
$begingroup$
Wolfram Language (Mathematica), 33 bytes
a@0=a@1=a@2=1;a@n_:=a[n-2]+a[n-3]
1-indexed, returns the nth term
Try it online!
answered 1 hour ago
J42161217J42161217
13.8k21253
$endgroup$
Wolfram Language (Mathematica), 33 bytes
a@0=a@1=a@2=1;a@n_:=a[n-2]+a[n-3]
1-indexed, returns the nth term
Try it online!
answered 1 hour ago
J42161217J42161217
13.8k21253
answered 1 hour ago
J42161217J42161217
13.8k21253
answered 1 hour ago
J42161217J42161217
13.8k21253
answered 1 hour ago
J42161217J42161217
13.8k21253
13.8k21253
add a comment |
add a comment |
$begingroup$
Python 2, 56 48 bytes
f=lambda n,a=1,b=1,c=1:n>2and f(n-1,b,c,a+b)or c
Try it online!
Returns nth value, 0-indexed.
answered 54 mins ago
Chas BrownChas Brown
5,2091523
$endgroup$
add a comment |
$begingroup$
Python 2, 56 48 bytes
f=lambda n,a=1,b=1,c=1:n>2and f(n-1,b,c,a+b)or c
Try it online!
Returns nth value, 0-indexed.
answered 54 mins ago
Chas BrownChas Brown
5,2091523
$endgroup$
add a comment |
$begingroup$
Python 2, 56 48 bytes
f=lambda n,a=1,b=1,c=1:n>2and f(n-1,b,c,a+b)or c
Try it online!
Returns nth value, 0-indexed.
answered 54 mins ago
Chas BrownChas Brown
5,2091523
$endgroup$
Python 2, 56 48 bytes
f=lambda n,a=1,b=1,c=1:n>2and f(n-1,b,c,a+b)or c
Try it online!
Returns nth value, 0-indexed.
answered 54 mins ago
Chas BrownChas Brown
5,2091523
answered 54 mins ago
Chas BrownChas Brown
5,2091523
answered 54 mins ago
Chas BrownChas Brown
5,2091523
answered 54 mins ago
Chas BrownChas Brown
5,2091523
5,2091523
add a comment |
add a comment |
$begingroup$
J, 26 bytes
0.5<.@+1.04535%~1.32472^<:
Try it online!
Uses the closed form formula.
answered 55 mins ago
JonahJonah
2,5911017
$endgroup$
add a comment |
$begingroup$
J, 26 bytes
0.5<.@+1.04535%~1.32472^<:
Try it online!
Uses the closed form formula.
answered 55 mins ago
JonahJonah
2,5911017
$endgroup$
add a comment |
$begingroup$
J, 26 bytes
0.5<.@+1.04535%~1.32472^<:
Try it online!
Uses the closed form formula.
answered 55 mins ago
JonahJonah
2,5911017
$endgroup$
J, 26 bytes
0.5<.@+1.04535%~1.32472^<:
Try it online!
Uses the closed form formula.
answered 55 mins ago
JonahJonah
2,5911017
edited 45 mins ago
answered 55 mins ago
JonahJonah
2,5911017
answered 55 mins ago
JonahJonah
2,5911017
answered 55 mins ago
JonahJonah
2,5911017
2,5911017
add a comment |
add a comment |
$begingroup$
Jelly, 11 bytes
5B+Ɲ2ị;Ʋ⁸¡Ḣ
Try it online!
0-indexed.
answered 40 mins ago
Erik the OutgolferErik the Outgolfer
33k429106
$endgroup$
$begingroup$
Can you specify whether this answer is 0-indexed or 1-indexed?
$endgroup$
– Tau
37 mins ago
$begingroup$
@Tau It's 0-indexed. I've edited it in.
$endgroup$
– Erik the Outgolfer
36 mins ago
add a comment |
$begingroup$
Jelly, 11 bytes
5B+Ɲ2ị;Ʋ⁸¡Ḣ
Try it online!
0-indexed.
answered 40 mins ago
Erik the OutgolferErik the Outgolfer
33k429106
$endgroup$
$begingroup$
Can you specify whether this answer is 0-indexed or 1-indexed?
$endgroup$
– Tau
37 mins ago
$begingroup$
@Tau It's 0-indexed. I've edited it in.
$endgroup$
– Erik the Outgolfer
36 mins ago
add a comment |
$begingroup$
Jelly, 11 bytes
5B+Ɲ2ị;Ʋ⁸¡Ḣ
Try it online!
0-indexed.
answered 40 mins ago
Erik the OutgolferErik the Outgolfer
33k429106
$endgroup$
Jelly, 11 bytes
5B+Ɲ2ị;Ʋ⁸¡Ḣ
Try it online!
0-indexed.
answered 40 mins ago
Erik the OutgolferErik the Outgolfer
33k429106
edited 36 mins ago
answered 40 mins ago
Erik the OutgolferErik the Outgolfer
33k429106
answered 40 mins ago
Erik the OutgolferErik the Outgolfer
33k429106
answered 40 mins ago
Erik the OutgolferErik the Outgolfer
33k429106
33k429106
$begingroup$
Can you specify whether this answer is 0-indexed or 1-indexed?
$endgroup$
– Tau
37 mins ago
$begingroup$
@Tau It's 0-indexed. I've edited it in.
$endgroup$
– Erik the Outgolfer
36 mins ago
add a comment |
$begingroup$
Can you specify whether this answer is 0-indexed or 1-indexed?
$endgroup$
– Tau
37 mins ago
$begingroup$
@Tau It's 0-indexed. I've edited it in.
$endgroup$
– Erik the Outgolfer
36 mins ago
$begingroup$
Can you specify whether this answer is 0-indexed or 1-indexed?
$endgroup$
– Tau
37 mins ago
$begingroup$
Can you specify whether this answer is 0-indexed or 1-indexed?
$endgroup$
– Tau
37 mins ago
$begingroup$
@Tau It's 0-indexed. I've edited it in.
$endgroup$
– Erik the Outgolfer
36 mins ago
$begingroup$
@Tau It's 0-indexed. I've edited it in.
$endgroup$
– Erik the Outgolfer
36 mins ago
add a comment |
$begingroup$
Jelly, 10 bytes
‘HŻcḤạ¥¥‘S
A monadic Link accepting n (1-indexed) which yields P(n).
Try it online!
answered 34 mins ago
Jonathan AllanJonathan Allan
53.7k535173
$endgroup$
add a comment |
$begingroup$
Jelly, 10 bytes
‘HŻcḤạ¥¥‘S
A monadic Link accepting n (1-indexed) which yields P(n).
Try it online!
answered 34 mins ago
Jonathan AllanJonathan Allan
53.7k535173
$endgroup$
add a comment |
$begingroup$
Jelly, 10 bytes
‘HŻcḤạ¥¥‘S
A monadic Link accepting n (1-indexed) which yields P(n).
Try it online!
answered 34 mins ago
Jonathan AllanJonathan Allan
53.7k535173
$endgroup$
Jelly, 10 bytes
‘HŻcḤạ¥¥‘S
A monadic Link accepting n (1-indexed) which yields P(n).
Try it online!
answered 34 mins ago
Jonathan AllanJonathan Allan
53.7k535173
answered 34 mins ago
Jonathan AllanJonathan Allan
53.7k535173
answered 34 mins ago
Jonathan AllanJonathan Allan
53.7k535173
answered 34 mins ago
Jonathan AllanJonathan Allan
53.7k535173
53.7k535173
add a comment |
add a comment |
$begingroup$
Haskell, 26 bytes
(l!!)
l=1:1:1:2:scanl(+)2l
Try it online! Outputs the n'th term zero-indexed.
I thought that the "obvious" recursive solution below would be unbeatable, but then I found this. It's similar to the classic golfy expression l=1:scanl(+)1l for the infinite Fibonacci list, but here the difference between adjacent elements is the term 4 positions back. We can more directly write l=1:1:zipWith(+)l(0:l), but that's longer.
If this challenge allowed infinite list output, we could cut the first line and have 20 bytes.
27 bytes
f n|n<3=1|1>0=f(n-2)+f(n-3)
Try it online!
answered 2 mins ago
xnorxnor
93.3k18190448
$endgroup$
add a comment |
$begingroup$
Haskell, 26 bytes
(l!!)
l=1:1:1:2:scanl(+)2l
Try it online! Outputs the n'th term zero-indexed.
I thought that the "obvious" recursive solution below would be unbeatable, but then I found this. It's similar to the classic golfy expression l=1:scanl(+)1l for the infinite Fibonacci list, but here the difference between adjacent elements is the term 4 positions back. We can more directly write l=1:1:zipWith(+)l(0:l), but that's longer.
If this challenge allowed infinite list output, we could cut the first line and have 20 bytes.
27 bytes
f n|n<3=1|1>0=f(n-2)+f(n-3)
Try it online!
answered 2 mins ago
xnorxnor
93.3k18190448
$endgroup$
add a comment |
$begingroup$
Haskell, 26 bytes
(l!!)
l=1:1:1:2:scanl(+)2l
Try it online! Outputs the n'th term zero-indexed.
I thought that the "obvious" recursive solution below would be unbeatable, but then I found this. It's similar to the classic golfy expression l=1:scanl(+)1l for the infinite Fibonacci list, but here the difference between adjacent elements is the term 4 positions back. We can more directly write l=1:1:zipWith(+)l(0:l), but that's longer.
If this challenge allowed infinite list output, we could cut the first line and have 20 bytes.
27 bytes
f n|n<3=1|1>0=f(n-2)+f(n-3)
Try it online!
answered 2 mins ago
xnorxnor
93.3k18190448
$endgroup$
Haskell, 26 bytes
(l!!)
l=1:1:1:2:scanl(+)2l
Try it online! Outputs the n'th term zero-indexed.
I thought that the "obvious" recursive solution below would be unbeatable, but then I found this. It's similar to the classic golfy expression l=1:scanl(+)1l for the infinite Fibonacci list, but here the difference between adjacent elements is the term 4 positions back. We can more directly write l=1:1:zipWith(+)l(0:l), but that's longer.
If this challenge allowed infinite list output, we could cut the first line and have 20 bytes.
27 bytes
f n|n<3=1|1>0=f(n-2)+f(n-3)
Try it online!
answered 2 mins ago
xnorxnor
93.3k18190448
answered 2 mins ago
xnorxnor
93.3k18190448
answered 2 mins ago
xnorxnor
93.3k18190448
answered 2 mins ago
xnorxnor
93.3k18190448
93.3k18190448
add a comment |
add a comment |
$begingroup$
C# (Visual C# Interactive Compiler), 34 bytes
int f(int g)=>g<3?1:f(g-2)+f(g-3);
Try it online!
answered 21 mins ago
Embodiment of IgnoranceEmbodiment of Ignorance
2,808127
$endgroup$
add a comment |
$begingroup$
C# (Visual C# Interactive Compiler), 34 bytes
int f(int g)=>g<3?1:f(g-2)+f(g-3);
Try it online!
answered 21 mins ago
Embodiment of IgnoranceEmbodiment of Ignorance
2,808127
$endgroup$
add a comment |
$begingroup$
C# (Visual C# Interactive Compiler), 34 bytes
int f(int g)=>g<3?1:f(g-2)+f(g-3);
Try it online!
answered 21 mins ago
Embodiment of IgnoranceEmbodiment of Ignorance
2,808127
$endgroup$
C# (Visual C# Interactive Compiler), 34 bytes
int f(int g)=>g<3?1:f(g-2)+f(g-3);
Try it online!
answered 21 mins ago
Embodiment of IgnoranceEmbodiment of Ignorance
2,808127
answered 21 mins ago
Embodiment of IgnoranceEmbodiment of Ignorance
2,808127
answered 21 mins ago
Embodiment of IgnoranceEmbodiment of Ignorance
2,808127
answered 21 mins ago
Embodiment of IgnoranceEmbodiment of Ignorance
2,808127
2,808127
add a comment |
add a comment |
$begingroup$
JavaScript (ES6), 23 bytes
Implements the recursive definition of A000931. Returns the $N$th term, 0-indexed.
f=n=>n<3||f(n-2)+f(n-3)
Try it online!
answered 20 mins ago
ArnauldArnauld
80.5k797333
$endgroup$
add a comment |
$begingroup$
JavaScript (ES6), 23 bytes
Implements the recursive definition of A000931. Returns the $N$th term, 0-indexed.
f=n=>n<3||f(n-2)+f(n-3)
Try it online!
answered 20 mins ago
ArnauldArnauld
80.5k797333
$endgroup$
add a comment |
$begingroup$
JavaScript (ES6), 23 bytes
Implements the recursive definition of A000931. Returns the $N$th term, 0-indexed.
f=n=>n<3||f(n-2)+f(n-3)
Try it online!
answered 20 mins ago
ArnauldArnauld
80.5k797333
$endgroup$
JavaScript (ES6), 23 bytes
Implements the recursive definition of A000931. Returns the $N$th term, 0-indexed.
f=n=>n<3||f(n-2)+f(n-3)
Try it online!
answered 20 mins ago
ArnauldArnauld
80.5k797333
edited 14 mins ago
answered 20 mins ago
ArnauldArnauld
80.5k797333
answered 20 mins ago
ArnauldArnauld
80.5k797333
answered 20 mins ago
ArnauldArnauld
80.5k797333
80.5k797333
add a comment |
add a comment |
$begingroup$
Japt -N, 12 bytes
<3ªßUµ2 +ß´U
Try it
answered 11 mins ago
Embodiment of IgnoranceEmbodiment of Ignorance
2,808127
$endgroup$
add a comment |
$begingroup$
Japt -N, 12 bytes
<3ªßUµ2 +ß´U
Try it
answered 11 mins ago
Embodiment of IgnoranceEmbodiment of Ignorance
2,808127
$endgroup$
add a comment |
$begingroup$
Japt -N, 12 bytes
<3ªßUµ2 +ß´U
Try it
answered 11 mins ago
Embodiment of IgnoranceEmbodiment of Ignorance
2,808127
$endgroup$
Japt -N, 12 bytes
<3ªßUµ2 +ß´U
Try it
answered 11 mins ago
Embodiment of IgnoranceEmbodiment of Ignorance
2,808127
answered 11 mins ago
Embodiment of IgnoranceEmbodiment of Ignorance
2,808127
answered 11 mins ago
Embodiment of IgnoranceEmbodiment of Ignorance
2,808127
answered 11 mins ago
Embodiment of IgnoranceEmbodiment of Ignorance
2,808127
2,808127
add a comment |
add a comment |
$begingroup$
Retina, 47 42 bytes
K`0¶1¶0
"$+"+`.+¶(.+)¶.+$
$&¶$.(*_$1*
6,G`
Try it online! Outputs the first n terms on separate lines. Explanation:
K`0¶1¶0
Replace the input with the terms for -2, -1 and 0.
"$+"+`.+¶(.+)¶.+$
$&¶$.(*_$1*
Generate the next n terms using the recurrence relation. *_ here is short for $&*_ which converts the (first) number in the match to unary, while $1* is short for $1*_ which converts the middle number to unary. The $.( returns the decimal sum of its unary arguments, i.e. the sum of the first and middle numbers.
6,G`
Discard the first six characters, i.e. the first three lines.
answered 11 mins ago
NeilNeil
82.6k745179
$endgroup$
add a comment |
$begingroup$
Retina, 47 42 bytes
K`0¶1¶0
"$+"+`.+¶(.+)¶.+$
$&¶$.(*_$1*
6,G`
Try it online! Outputs the first n terms on separate lines. Explanation:
K`0¶1¶0
Replace the input with the terms for -2, -1 and 0.
"$+"+`.+¶(.+)¶.+$
$&¶$.(*_$1*
Generate the next n terms using the recurrence relation. *_ here is short for $&*_ which converts the (first) number in the match to unary, while $1* is short for $1*_ which converts the middle number to unary. The $.( returns the decimal sum of its unary arguments, i.e. the sum of the first and middle numbers.
6,G`
Discard the first six characters, i.e. the first three lines.
answered 11 mins ago
NeilNeil
82.6k745179
$endgroup$
add a comment |
$begingroup$
Retina, 47 42 bytes
K`0¶1¶0
"$+"+`.+¶(.+)¶.+$
$&¶$.(*_$1*
6,G`
Try it online! Outputs the first n terms on separate lines. Explanation:
K`0¶1¶0
Replace the input with the terms for -2, -1 and 0.
"$+"+`.+¶(.+)¶.+$
$&¶$.(*_$1*
Generate the next n terms using the recurrence relation. *_ here is short for $&*_ which converts the (first) number in the match to unary, while $1* is short for $1*_ which converts the middle number to unary. The $.( returns the decimal sum of its unary arguments, i.e. the sum of the first and middle numbers.
6,G`
Discard the first six characters, i.e. the first three lines.
answered 11 mins ago
NeilNeil
82.6k745179
$endgroup$
Retina, 47 42 bytes
K`0¶1¶0
"$+"+`.+¶(.+)¶.+$
$&¶$.(*_$1*
6,G`
Try it online! Outputs the first n terms on separate lines. Explanation:
K`0¶1¶0
Replace the input with the terms for -2, -1 and 0.
"$+"+`.+¶(.+)¶.+$
$&¶$.(*_$1*
Generate the next n terms using the recurrence relation. *_ here is short for $&*_ which converts the (first) number in the match to unary, while $1* is short for $1*_ which converts the middle number to unary. The $.( returns the decimal sum of its unary arguments, i.e. the sum of the first and middle numbers.
6,G`
Discard the first six characters, i.e. the first three lines.
answered 11 mins ago
NeilNeil
82.6k745179
edited 1 min ago
answered 11 mins ago
NeilNeil
82.6k745179
answered 11 mins ago
NeilNeil
82.6k745179
answered 11 mins ago
NeilNeil
82.6k745179
82.6k745179
add a comment |
add a comment |
If this is an answer to a challenge…
…Be sure to follow the challenge specification. However, please refrain from exploiting obvious loopholes. Answers abusing any of the standard loopholes are considered invalid. If you think a specification is unclear or underspecified, comment on the question instead.
…Try to optimize your score. For instance, answers to code-golf challenges should attempt to be as short as possible. You can always include a readable version of the code in addition to the competitive one.
Explanations of your answer make it more interesting to read and are very much encouraged.…Include a short header which indicates the language(s) of your code and its score, as defined by the challenge.
More generally…
…Please make sure to answer the question and provide sufficient detail.
…Avoid asking for help, clarification or responding to other answers (use comments instead).
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$begingroup$
Sandbox post can be found here.
$endgroup$
– Tau
1 hour ago
1
$begingroup$
14(0-indexed) is shown as outputting28while I believe it should yield37$endgroup$
– Jonathan Allan
45 mins ago
$begingroup$
@JonathanAllan yes, you are correct. I fixed the last two test cases for $N$th term but not that one. The post has been edited.
$endgroup$
– Tau
43 mins ago