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 A151059 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), (0, 0, -1), (0, 1, 0), (1, 0, 0), (1, 1, 0)}. 0

%I #4 Sep 03 2022 23:45:05

%S 1,3,10,38,151,625,2675,11697,52043,234891,1072130,4939000,22930993,

%T 107169943,503692524,2378872670,11282929599,53714328463,256558536980,

%U 1229004648862,5902782031035,28417105740879,137095496703643,662675127371465,3208756135885231,15561983660317885,75583524112506556

%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), (0, 0, -1), (0, 1, 0), (1, 0, 0), (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, 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]]; 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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Last modified May 21 00:14 EDT 2024. Contains 372720 sequences. (Running on oeis4.)