A148510 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, -1), (-1, -1, 1), (-1, 0, 1), (-1, 1, 0), (1, 0, 0)}.

1, 1, 3, 5, 17, 34, 131, 293, 1193, 2846, 11849, 29446, 125418, 321788, 1397379, 3676149, 16136815, 43251008, 191531227, 521232376, 2328712424, 6420749688, 28872313915, 80469169189, 363621787823, 1022657892404, 4643406285581, 13164136578458, 60021459192113, 171355580107291, 783849426144354, 2251422863051399

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A148507 A148508 A148509 * A215396 A130844 A148511

Adjacent sequences: A148507 A148508 A148509 * A148511 A148512 A148513

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved