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%I A151442 #7 Jan 01 2024 02:41:08
%S A151442 1,1,2,5,13,37,111,348,1115,3690,12437,42646,148530,523835,1868356,
%T A151442 6729649,24454173,89552497,330263689,1225741014,4575462854,
%U A151442 17169395749,64738926261,245187658138,932406910922,3559219448897,13634163069767,52398809327631,201994189232865,780899820381385,3027006453635929
%N A151442 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), (0, -1), (0, 1), (1, -1), (1, 0)}.
%H A151442 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 A151442 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[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 A151442 nonn,walk
%O A151442 0,3
%A A151442 _Manuel Kauers_, Nov 18 2008

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