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 A151318 #16 Jun 02 2025 01:11:55
%S A151318 1,3,13,55,249,1131,5253,24543,115825,549331,2620029,12543367,
%T A151318 60270697,290423355,1403088885,6793370415,32956254945,160152588195,
%U A151318 779470975725,3798948989655,18538237315545,90565618791435,442899758973285,2167985089576575,10621425660150609,52078139149834611,255533719072119133
%N A151318 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 1), (-1, 0), (0, 1), (1, 0), (1, 1)}.
%H A151318 Alin Bostan, <a href="https://citeseerx.ist.psu.edu/pdf/749aef4c6f3668e652b5074e5268346ccecc88c9">Computer Algebra for Lattice Path Combinatorics</a>, Seminaire de Combinatoire Ph. Flajolet, March 28 2013.
%H A151318 Alin Bostan, Andrew Elvey Price, Anthony John Guttmann, and Jean-Marie Maillard, <a href="https://arxiv.org/abs/2001.00393">Stieltjes moment sequences for pattern-avoiding permutations</a>, arXiv:2001.00393 [math.CO], 2020.
%H A151318 Mireille Bousquet-Mélou and Marni Mishna, <a href="https://arxiv.org/abs/:0810.4387">Walks with small steps in the quarter plane</a>, >arXiv:0810.4387 [math.CO], 2008.
%H A151318 Alin Bostan and Manuel Kauers, <a href="https://arxiv.org/abs/:0811.2899">Automatic Classification of Restricted Lattice Walks</a>, >arXiv:0811.2899 [math.CO], 2008.
%H A151318 Paveł Szabłowski, <a href="https://cdm.ucalgary.ca/article/view/76214">Beta distributions whose moment sequences are related to integer sequences listed in the OEIS</a>, Contrib. Disc. Math. (2024) Vol. 19, No. 4, 85-109. See p. 99.
%t A151318 aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[-1 + i, j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]
%K A151318 nonn,walk
%O A151318 0,2
%A A151318 _Manuel Kauers_, Nov 18 2008