%I #7 Jan 01 2024 02:44:02
%S 1,2,11,78,632,5547,51343,493561,4880756,49335396,507489524,
%T 5295338330,55912919498,596320327868,6414558641802,69513860916094,
%U 758204411559337,8317193553286408,91698991538371147,1015583349964628187,11293570968982354094,126049685734959507338,1411563666881071642920
%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 2 n steps taken from {(-1, 1), (1, -1), (1, 0), (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[-1 + i, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n]]; Table[Sum[aux[0, k, 2 n], {k, 0, 2 n}], {n, 0, 25}]
%K nonn,walk
%O 0,2
%A _Manuel Kauers_, Nov 18 2008
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