A150163 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, 0, 0), (0, 0, -1), (0, 1, 1), (1, 0, 0)}.

1, 2, 6, 20, 75, 286, 1150, 4676, 19516, 82325, 352551, 1523146, 6642454, 29173778, 128957103, 573244772, 2560570574, 11488400595, 51743747415, 233877257170, 1060458726444, 4822197619857, 21985847689686, 100479988520140, 460236805646737, 2112349827532275, 9713396499616699, 44744248639000013

Offset

0,2

Links

Table of n, a(n) for n=0..27.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

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[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, 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}]

Crossrefs

Sequence in context: A150160 A150161 A150162 * A150164 A150165 A148482

Adjacent sequences: A150160 A150161 A150162 * A150164 A150165 A150166

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved