A150578 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, 1), (0, 1, 1), (1, 0, -1), (1, 0, 1)}.

1, 2, 7, 26, 109, 449, 1995, 8648, 39542, 177391, 824142, 3780180, 17757683, 82638051, 391512994, 1840788102, 8778125385, 41599169813, 199370832862, 950717604657, 4574750880399, 21924045003490, 105846504118961, 509316666679058, 2465797422256411, 11904956817171765, 57773578111490989, 279724927288607769

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

Crossrefs

Sequence in context: A150576 A150577 A302184 * A150579 A093638 A150580

Adjacent sequences: A150575 A150576 A150577 * A150579 A150580 A150581

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved