%I #4 Dec 27 2023 21:49:06
%S 1,3,12,47,218,965,4599,21221,102970,486505,2382781,11426421,56269394,
%T 272411885,1346576694,6562913261,32525351076,159299916487,
%U 790932819647,3887965109601,19330600629450,95291594229807,474275668773044,2343180181071035,11671642055093232,57766754545789109,287925843112694359
%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, -1), (-1, 1, 1), (1, 0, 0), (1, 0, 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[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 1 + 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 0,2
%A _Manuel Kauers_, Nov 18 2008
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