A149856 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, 1), (-1, 1, 0), (0, 0, 1), (1, 0, 0)}.

1, 2, 5, 13, 37, 119, 397, 1364, 4718, 16679, 60629, 223411, 831697, 3115490, 11781657, 45056702, 173446087, 671335261, 2610604193, 10205624491, 40127858406, 158396721706, 627451787342, 2493938507817, 9946087760078, 39803742369745, 159716582107213, 642487259246869, 2590943237172682

Offset

0,2

Links

Table of n, a(n) for n=0..28.

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, 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] + 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: A339039 A205544 A149855 * A320175 A064384 A148302

Adjacent sequences: A149853 A149854 A149855 * A149857 A149858 A149859

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved