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 A151265 #24 Apr 19 2025 03:38:22
%S A151265 1,1,3,7,17,47,125,333,939,2597,7183,20505,57859,163201,469795,
%T A151265 1341775,3830529,11092823,31940165,91927379,267406401,774447755,
%U A151265 2242022721,6544458687,19036737381,55354815639,162028272261,472921269031,1379896701413,4048204328607,11848014062621,34665885291485
%N A151265 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 0), (0, -1), (1, 1)}.
%D A151265 Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, page 997.
%H A151265 Alois P. Heinz, <a href="/A151265/b151265.txt">Table of n, a(n) for n = 0..1000</a>
%H A151265 M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, <a href="http://arxiv.org/abs/0810.4387">ArXiv 0810.4387</a>.
%H A151265 Alin Bostan, <a href="https://specfun.inria.fr/bostan/HDR.pdf">Calcul Formel pour la Combinatoire des Marches</a> [The text is in English], Habilitation à Diriger des Recherches, Laboratoire d'Informatique de Paris Nord, Université Paris 13, December 2017.
%H A151265 A. 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 A151265 A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, <a href="http://arxiv.org/abs/0811.2899">ArXiv 0811.2899</a>.
%F A151265 a(n) == 1 (mod 2). - _Alois P. Heinz_, Jul 12 2021
%t A151265 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[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}]
%Y A151265 Column k=2 of A335570.
%K A151265 nonn,walk
%O A151265 0,3
%A A151265 _Manuel Kauers_, Nov 18 2008