This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A302186 #17 Nov 29 2024 07:36:02 %S A302186 1,3,11,44,188,842,3911,18692,91412,455540,2306028,11829424,61375408, %T A302186 321583108,1699500055,9049714852,48513809796,261638920412, %U A302186 1418673379052,7730011715760,42305916178288,232475082183544,1282208011668988,7096065370945168,39394821683770960,219341739839760912 %N A302186 Number of 3D walks of type ace. %C A302186 See Dershowitz (2017) for precise definition. %H A302186 Nachum Dershowitz, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Dershowitz/dersh3.html">Touchard's Drunkard</a>, Journal of Integer Sequences, Vol. 20 (2017), #17.1.5. %F A302186 Binomial transform of A145847. - _Mélika Tebni_, Nov 29 2024 %o A302186 (Python) %o A302186 from math import comb as binomial %o A302186 def C(n): return (binomial(2*n, n)//(n+1)) # Catalan numbers %o A302186 def row(n: int) -> list[int]: %o A302186 return sum(binomial(n, k)*sum(binomial(k, j)*C((j+1)//2)*C(j//2)*(2*(j//2)+1) for j in range(k+1)) for k in range(n+1)) %o A302186 for n in range(26): print(row(n)) # _Mélika Tebni_, Nov 29 2024 %Y A302186 Cf. A000108, A000984, A002212, A002896, A005572, A026375, A064037, A081671, A138547, A145847, A145867 (number of 3D walks of type acd), A150500, A202814. %K A302186 nonn,walk %O A302186 0,2 %A A302186 _N. J. A. Sloane_, Apr 09 2018 %E A302186 a(12)-a(25) from _Mélika Tebni_, Nov 29 2024