A148166 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, 1, 0), (0, 0, 1), (0, 1, -1), (1, -1, 1)}.

1, 1, 2, 4, 11, 31, 100, 336, 1164, 4208, 15469, 58466, 225190, 880301, 3496564, 14038923, 56997583, 233660341, 965627303, 4022453551, 16868310880, 71177273008, 302067154265, 1288436846350, 5522066045103, 23769932778195, 102728465777956, 445638762353076, 1939857841809377, 8471446919675513

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, -1 + j, 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: A364594 A213091 A148165 * A148167 A148168 A004251

Adjacent sequences: A148163 A148164 A148165 * A148167 A148168 A148169

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved