A151184 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, 1, 0), (1, 1, -1), (1, 1, 0), (1, 1, 1)}

1, 3, 12, 51, 227, 1032, 4771, 22303, 105172, 499224, 2382287, 11417067, 54911577, 264895775, 1281143686, 6209829047, 30157663079, 146707096810, 714753840271, 3486934763359, 17031540144399, 83279152024797, 407612515967400, 1996870740970424, 9790634214005765, 48039818387010011, 235882744914207304

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, 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: A180898 A110167 A151317 * A256334 A377582 A151185

Adjacent sequences: A151181 A151182 A151183 * A151185 A151186 A151187

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved