A151060 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), (0, 1, -1), (0, 1, 0), (1, 0, 0), (1, 1, 0)}.

1, 3, 10, 38, 151, 629, 2708, 11895, 53247, 241581, 1108029, 5129837, 23924429, 112292988, 529925578, 2512275399, 11958499231, 57122301771, 273699037655, 1315019659000, 6333543965110, 30570993733509, 147851445115109, 716327583117247, 3476145001287003, 16893568584074417, 82210551916213699

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[-1 + i, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[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: A083692 A308124 A151059 * A151061 A109085 A259690

Adjacent sequences: A151057 A151058 A151059 * A151061 A151062 A151063

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved