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A148395 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), (0, 0, -1), (1, 0, -1), (1, 0, 0)}. 0

%I #4 Jan 01 2024 00:53:24

%S 1,1,2,5,16,53,194,678,2540,9864,39339,159002,650824,2696290,11362478,

%T 48339341,207535853,897905427,3913431910,17176437470,75847364805,

%U 336777968274,1503202127905,6739922000073,30346283721419,137170213293591,622379744415404,2833871341615016,12943682517721161

%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), (0, 0, -1), (1, 0, -1), (1, 0, 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, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, j, 1 + 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 0,3

%A _Manuel Kauers_, Nov 18 2008

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)