A148121 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, -1, 1), (-1, 0, 1), (0, 1, 0), (1, -1, 0)}.

1, 1, 2, 4, 11, 26, 70, 211, 637, 1898, 5975, 19499, 62042, 199992, 673153, 2273986, 7603164, 25960343, 90166835, 310587571, 1071398522, 3766507591, 13307211972, 46786797955, 165853350155, 593866808974, 2121950884159, 7579020049467, 27310183812764, 98847426975641, 357157376532021, 1294868619965046

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, 1 + j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A148118 A148119 A148120 * A148122 A148123 A148124

Adjacent sequences: A148118 A148119 A148120 * A148122 A148123 A148124

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved