A148154 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), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 4, 11, 30, 95, 298, 1006, 3389, 11909, 41892, 151248, 547242, 2013692, 7428090, 27714657, 103659360, 390818670, 1476869632, 5613303220, 21379805046, 81781927372, 313417411878, 1205079525721, 4641169988978, 17920658283987, 69296999144435, 268512038320354, 1041768167687090, 4048556883494679

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, j, 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: A148151 A148152 A148153 * A148155 A007719 A148156

Adjacent sequences: A148151 A148152 A148153 * A148155 A148156 A148157

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved