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 A151093 #14 Feb 07 2025 09:25:35
%S A151093 1,3,11,43,177,751,3263,14421,64613,292639,1337295,6156635,28523245,
%T A151093 132861795,621783139,2921870183,13780286589,65201337703,309392108399,
%U A151093 1471944790095,7019341847821,33545270688803,160625969491971,770511786145853,3702199537395337,17815681545802971,85853558110277963
%N A151093 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 0, -1), (1, 0, 0), (1, 0, 1), (1, 1, 0)}.
%H A151093 Alin Bostan and Manuel Kauers, <a href="http://arxiv.org/abs/0811.2899">Automatic Classification of Restricted Lattice Walks</a>, arXiv:0811.2899 [math.CO], 2008-2009.
%H A151093 Mélika Tebni, <a href="http://retoz.free.fr/decembre2024.pdf">Fonctions de Bessel et cheminements en 3D</a>, Dec 2024.
%F A151093 E.g.f.: (BesselI(0, 2*x) + BesselI(1, 2*x))^2*exp(x). - _Mélika Tebni_, Feb 07 2025
%t A151093 aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
%K A151093 nonn,walk
%O A151093 0,2
%A A151093 _Manuel Kauers_, Nov 18 2008