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%I #4 Jan 01 2024 00:49:25
%S 1,1,2,5,16,42,147,454,1628,5425,20178,70153,268235,962420,3748820,
%T 13809050,54492862,204977746,817599476,3126108027,12586411942,
%U 48758462507,197878414706,775091653268,3166333356578,12521930286700,51439036172347,205114689753037,846727775491103,3400496099226738
%N 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), (-1, 1, 0), (0, 1, 1), (1, -1, 0)}.
%H 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 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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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 nonn,walk
%O 0,3
%A _Manuel Kauers_, Nov 18 2008
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