A148275 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, -1), (-1, 1, 1), (1, -1, 0), (1, 0, 0)}.

1, 1, 2, 4, 15, 40, 159, 477, 1955, 6329, 27222, 93788, 412542, 1474861, 6579591, 24261248, 109884004, 415728514, 1901528670, 7332329870, 33799600692, 132520569402, 615348352600, 2447006155439, 11425358766922, 45967911583713, 215656885564443, 876735796325931, 4130899475279367

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A148272 A148273 A148274 * A148276 A148277 A148278

Adjacent sequences: A148272 A148273 A148274 * A148276 A148277 A148278

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved