A148875 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, 1), (-1, 1, 1), (0, 1, -1), (1, -1, 0), (1, 0, 0)}.

1, 1, 3, 8, 29, 104, 405, 1634, 6788, 28922, 125559, 554058, 2474920, 11188064, 51025586, 234609810, 1086430868, 5061096381, 23702973326, 111544459533, 527097647852, 2500077258967, 11898645626830, 56798990784424, 271874618573959, 1304627798728260, 6274476702322705, 30238642580810987

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, j, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A148873 A148874 A022017 * A338306 A148876 A245889

Adjacent sequences: A148872 A148873 A148874 * A148876 A148877 A148878

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved