A148674 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), (-1, -1, 1), (0, 0, -1), (0, 1, -1), (1, 1, 0)}

1, 1, 3, 7, 21, 65, 205, 693, 2359, 8239, 29515, 106499, 391467, 1455087, 5452595, 20672471, 78900633, 303359513, 1175020613, 4574684005, 17916257965, 70522908505, 278795140965, 1107201637121, 4413934773601, 17660667666925, 70913992184321, 285628248472061, 1153968725090537, 4675436105737789

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[i, -1 + 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, 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: A121797 A109361 A052805 * A148675 A148676 A105864

Adjacent sequences: A148671 A148672 A148673 * A148675 A148676 A148677

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved