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%I #9 Mar 25 2020 15:58:29
%S 1,3,13,55,249,1131,5253,24543,115825,549331,2620029,12543367,
%T 60270697,290423355,1403088885,6793370415,32956254945,160152588195,
%U 779470975725,3798948989655,18538237315545,90565618791435,442899758973285,2167985089576575,10621425660150609,52078139149834611,255533719072119133
%N 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 A. Bostan, <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.410.1160&rep=rep1&type=pdf">Computer Algebra for Lattice Path Combinatorics</a>, Seminaire de Combinatoire Ph. Flajolet, March 28 2013.
%H Alin Bostan, Andrew Elvey Price, Anthony John Guttmann, 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 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 A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, <a href="http://arxiv.org/abs/0811.2899">ArXiv 0811.2899</a>.
%t 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 nonn,walk
%O 0,2
%A _Manuel Kauers_, Nov 18 2008
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