A148155 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), (0, 0, 1), (0, 1, -1), (1, -1, 1)}.

1, 1, 2, 4, 11, 30, 95, 301, 1009, 3456, 12224, 44125, 162233, 605635, 2292782, 8784156, 34020119, 132973231, 524230617, 2082337971, 8329063745, 33523745895, 135704089247, 552226170127, 2258059087302, 9274549193981, 38251031428465, 158365187672308, 658005514127674, 2743136216360006

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A148152 A148153 A148154 * A007719 A148156 A148157

Adjacent sequences: A148152 A148153 A148154 * A148156 A148157 A148158

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved