A150216 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), (0, 0, -1), (0, 1, -1), (0, 1, 0), (1, 0, 1)}.

1, 2, 6, 21, 82, 315, 1270, 5286, 22312, 94860, 409872, 1789776, 7860018, 34740429, 154655188, 691888680, 3107165282, 14012949053, 63443464419, 288098351357, 1311858162243, 5990296752848, 27420393186253, 125777294226442, 578105201541479, 2662283577333729, 12281269412823336, 56742405316089524

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A150214 A150215 A328434 * A150217 A150218 A150219

Adjacent sequences: A150213 A150214 A150215 * A150217 A150218 A150219

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved