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%I #7 Mar 08 2023 12:37:14
%S 1,0,2,2,8,22,56,192,558,1746,5850,18108,61450,202310,672880,2302762,
%T 7740494,26610514,91536712,315135590,1097812420,3815592588,
%U 13349580584,46872331154,164755197130,582028252912,2058703367868,7302057111804,25970243832668,92497076203672,330283889496320,1181287444107564
%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, 0), (0, -1), (1, 1)}.
%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, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, 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 0,3
%A _Manuel Kauers_, Nov 18 2008
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