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%I A149513 #4 Jan 20 2024 14:48:52
%S A149513 1,1,5,11,47,155,601,2255,8981,34599,141187,561435,2304911,9360735,
%T A149513 38838245,159466743,667227123,2769683191,11647989101,48731215829,
%U A149513 206061404939,867147480815,3682148906021,15580433317623,66380446504309,282052095021781,1205576096388165,5140839868168313
%N A149513 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, 1, -1), (1, -1, -1), (1, 1, 1)}.
%H A149513 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 A149513 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, 1 + j, 1 + k, -1 + n] + aux[i, -1 + 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 A149513 nonn,walk
%O A149513 0,3
%A A149513 _Manuel Kauers_, Nov 18 2008

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