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%I A148350 #4 Jan 01 2024 00:46:39
%S A148350 1,1,2,5,15,42,141,454,1636,5654,21372,77839,304105,1149623,4605049,
%T A148350 17911778,73142360,290931536,1206443012,4886121626,20518294930,
%U A148350 84344339293,357919513388,1489741008146,6378159512931,26830071268609,115748486759273,491362556375669,2133872051606574
%N A148350 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 0, 1), (1, 0, -1), (1, 0, 0), (1, 1, -1)}.
%H A148350 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 A148350 aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
%K A148350 nonn,walk
%O A148350 0,3
%A A148350 _Manuel Kauers_, Nov 18 2008

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