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%I A149951 #2 Mar 30 2012 18:54:16
%S A149951 1,2,5,15,50,176,646,2452,9549,37961,153511,629732,2614885,10972374,
%T A149951 46463260,198334111,852639288,3688754625,16049389276,70187680379,
%U A149951 308375520541,1360617913209,6026613738270,26788857783196,119469665596501,534412213485831,2397257900073820,10781700156879226
%N A149951 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, -1, 1), (0, 0, 1), (0, 1, 0), (1, 1, -1)}
%H A149951 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 A149951 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[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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 A149951 nonn,walk
%O A149951 0,2
%A A149951 _Manuel Kauers_, Nov 18 2008

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