A151132 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, 0, -1), (0, 1, 0), (0, 1, 1), (1, 0, 1)}

1, 3, 11, 45, 198, 887, 4047, 18768, 87949, 415183, 1972722, 9422395, 45189129, 217479786, 1049796775, 5080295503, 24638793232, 119724644589, 582747344130, 2840693292165, 13865869687615, 67762568930632, 331513625649517, 1623447018209726, 7957240718117833, 39033855586296611, 191622276472893138

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, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 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: A001003 A080243 A151131 * A200075 A187764 A151133

Adjacent sequences: A151129 A151130 A151131 * A151133 A151134 A151135

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved