A148187 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), (0, 0, -1), (0, 1, 0), (1, -1, 0)}.

1, 1, 2, 4, 12, 30, 93, 267, 883, 2804, 9586, 32445, 114178, 404537, 1462307, 5349537, 19800648, 74146404, 280190689, 1068734524, 4110516365, 15922071713, 62145913561, 243952955828, 964002185825, 3828747254167, 15290516388596, 61355753916594, 247316160801343, 1001327469687834, 4069825140933222

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, 1 + j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 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: A308556 A148186 A006948 * A148188 A148189 A148190

Adjacent sequences: A148184 A148185 A148186 * A148188 A148189 A148190

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved