A148339 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, 0), (-1, -1, 1), (0, 1, -1), (1, 0, 1)}.

1, 1, 2, 5, 15, 38, 126, 403, 1267, 4364, 15337, 51008, 186733, 677566, 2371655, 8911984, 33363459, 120099472, 461730365, 1762385298, 6489781432, 25333729456, 98240077694, 367777089473, 1453543853992, 5704662375120, 21642574662270, 86368923368039, 342309093506743, 1312621073998531, 5280365528689306

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A245961 A034522 A276720 * A148340 A148341 A258121

Adjacent sequences: A148336 A148337 A148338 * A148340 A148341 A148342

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved