A151200 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, 0), (0, 1, 1), (1, 0, 1), (1, 1, -1), (1, 1, 0)}.

1, 3, 12, 53, 242, 1138, 5434, 26199, 127376, 622268, 3053438, 15029014, 74157258, 366653302, 1815673654, 9003329553, 44692323636, 222054482004, 1104120942040, 5493564170090, 27348418661820, 136212033035508, 678698740724990, 3382928052071028, 16867212596433914, 84122447519298902

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, -1 + j, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A370023 A151198 A151199 * A151201 A151202 A151203

Adjacent sequences: A151197 A151198 A151199 * A151201 A151202 A151203

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved