A148494 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, 0, 0), (-1, 1, 1), (0, 0, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 2, 6, 21, 81, 330, 1379, 5943, 26192, 117531, 534629, 2459298, 11413397, 53365727, 251094785, 1187772059, 5644400172, 26929252668, 128922697132, 619083834686, 2980784061799, 14386078118494, 69578413395120, 337156931334842, 1636565633906717, 7956237339951546, 38734085204628560

Offset

0,3

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, -1 + j, 1 + k, -1 + n] + aux[-1 + 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, 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: A148492 A150211 A148493 * A150212 A150213 A279565

Adjacent sequences: A148491 A148492 A148493 * A148495 A148496 A148497

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved