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3 votes

Output the sign

Trilangle, 21 bytes ?\<'1(0@'^\.!_@>'0.(# Try it in the online interpreter! Unfolds to this: ...
  • 1,768
1 vote

Output the sign

Thunno, 2 bytes za Attempt This Online! Built-in. Works on lists. Thunno D, 3 bytes ZA, ...
  • 9,121
1 vote

Collapse consecutive integers

Vyxal, 23 bytes D0J¨pε⁽ṅḋ•ƛL⁰≥[₍ht\-Y}f Try it Online! 23 bytes seems to be the standard here, so I figured I'd add my own 23 byter. Takes ...
  • 27.6k
0 votes

As Easy as One-Two-Three

Thunno, \$ 8 \log_{256}(96)\approx \$ 6.58 bytes dz[11dA= Attempt This Online! Port of Emigna's 05AB1E answer.
  • 9,121
0 votes

As Easy as One-Two-Three

Arturo, 27 bytes $[n][∧12=n%111n<=>13 789] Try it ...
  • 16.7k
1 vote

As Easy as One-Two-Three

Pyt, 11 bytes ą₋Đ₋¬⇹Ʃ2=∧Π Try it online! ...
0 votes

Stay away from zero

Pyt, 3 bytes 1←↑ Try it online! 1 push 1 ← get input ↑ get maximum value on the stack; implicit print
3 votes

A Fine sequence with fine interpretations

Jelly, 7 bytes ~cŻÄÆmA This calculates abs(mean(cumsum(choose(-n-1, [0..n])))). Try it online! The "negative binomial ...
  • 67k
4 votes

A Fine sequence with fine interpretations

Python 2, 49 bytes Prints the sequence indefinitely. x=c=n=1 while 1:print x;n+=1;c=c*4-c*6/n;x=c-x>>1 Try it online! Based on the Sage program at the end ...
  • 20.4k
1 vote

A Fine sequence with fine interpretations

Pyt, 32 bytes Đ⁺Đř⁻ĐĐ05Ș↔+2ř*⇹ɐ-Á⇹ć⇹⁺*⇹1~⇹^·⇹/ Try it online! Naive implementation of the formula in the question. The following walkthrough of the code is worked ...
2 votes

A Fine sequence with fine interpretations

Factor + koszul math.combinatorics, 69 bytes [ 4 dupn + [a,b] [ -1^ -rot nCk * ] with map-index cum-sum mean abs ] Try it ...
  • 16.7k
1 vote

A Fine sequence with fine interpretations

Charcoal, 25 bytes ⊞υ¹≔¹θFN≔⊘⁻↨⊞OυΣ×⮌υυ⁰θθIθ Attempt This Online! Link is to verbose version of code. Explanation: ⊞υ¹ Start ...
  • 156k
4 votes

A Fine sequence with fine interpretations

Jelly, 12 11 bytes ḤrcµJNÐeḋ:L Try it online! Port of emanresu A's golf to mathcat's Vyxal solution. ...
6 votes

A Fine sequence with fine interpretations

Vyxal, 22 10 7 bytes -12 bytes by emanresu A (double welp) -3 bytes by alephalpha using a clever approach ꜝ$ʀƈ¦ṁȧ Try it Online! How it works ...
  • 7,457
4 votes

A Fine sequence with fine interpretations

05AB1E, 22 21 14 bytes xŸIc2Å€(}ηOÅAÄ Port of @mathcat's Vyxal answer, so make sure to upvote him as well! Uses the formula: $$G_{n,k} = (-1)^{(k+1)}\binom{k}{n} + ...
4 votes

A Fine sequence with fine interpretations

Python 3, 61 bytes f=lambda n,v=1:sum(f(i,0)*f(n+~i,v)for i in range(v,n))or 1-n Try it online! JavaScript (Node.js), 50 bytes ...
  • 32.8k
3 votes

A Fine sequence with fine interpretations

PARI/GP, 36 bytes n->Vec(2/(1+2*x+sqrt(1-4*x+O(x^n)))) Attempt This Online! Using the generating function. PARI/GP, 39 bytes ...
  • 41.8k
5 votes

A Fine sequence with fine interpretations

HOPS, 19 bytes C=1+x*C^2;C/(1+x*C) Attempt This Online! The generating function of the Catalan numbers satisfies \$C(x)=1+x\ C(x)^2\$. The generating function of ...
  • 41.8k
1 vote

Moving modest minimum

Desmos, 26 bytes f(x)=x.sort[1+0^{x-x.min}] Try it on Desmos! Port of this answer.
  • 2,750
4 votes

A Fine sequence with fine interpretations

Desmos, 46 41 bytes f(n)=-∑_{k=1}^n(-1)^kknCr(2n-k-1,n-k)/n A port of the explicit formula but with one-indexing instead of zero-indexing. Try It On Desmos! Try It ...
  • 11.2k
6 votes

A Fine sequence with fine interpretations

Python 2, 58 bytes i=a=1;b=0 while 1:print a;i+=1;a,b=2*b+7*a/2-(2*a+b)*3/i,a Try it online! Prints the sequence endlessly. The method substitutes \$C_n = 2F_n + ...
  • 13.7k
4 votes

A Fine sequence with fine interpretations

JavaScript (ES6), 48 bytes Returns the \$n\$-th term (0-indexed). Inspired by the Catalan recurrence pointed out by Sisyphus. ...
  • 179k
1 vote

Moving modest minimum

Japt, 8 bytes £éYn)Årm Try it Try all test cases Explanation: ...
1 vote

Moving modest minimum

Arturo, 28 bytes $[a][map a=>[min a--.once&]] Try it ...
  • 16.7k
0 votes

N-dimensional N^N array filled with N

Arturo, 20 bytes $=>[@.of:@.of:<=<=&] Try it Huh? In Arturo, you can initialize a block of values like this: ...
  • 16.7k

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