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%I #5 Dec 04 2016 13:57:04
%S 1,0,1,1,5,6,33,66,262,688,2614,7630,28372,91490,333166,1139686,
%T 4172274,14771196,54529720,198319758,738538816,2738271072,10302251312,
%U 38749276416,147201935416,560210700982,2146843198772,8250106899418,31870249952754,123485120302378,480468887927340,1874991897193156
%N Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, -1), (-1, 1), (0, -1), (1, -1), (1, 0)}
%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>.
%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, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]
%K nonn,walk
%O 0,5
%A _Manuel Kauers_, Nov 18 2008
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