A148124 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, 0, 1), (-1, 1, -1), (0, 0, -1), (1, 0, 0)}.

1, 1, 2, 4, 11, 26, 75, 209, 628, 1883, 5951, 18686, 60927, 199714, 664361, 2240274, 7643810, 26202820, 91110947, 318663775, 1120228682, 3977941573, 14197123531, 50843366658, 183631585543, 665691578173, 2420005200256, 8859024855551, 32527716161891, 119696589287840, 443083822620602, 1644126404907612

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A148121 A148122 A148123 * A148125 A148126 A148127

Adjacent sequences: A148121 A148122 A148123 * A148125 A148126 A148127

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved