A149994 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), (-1, 0, -1), (-1, 1, 1), (0, 1, 1), (1, 0, 0)}.

1, 2, 5, 17, 59, 214, 803, 3056, 11895, 47004, 187667, 756321, 3069385, 12542846, 51578053, 213150329, 884724627, 3686093838, 15410995185, 64642971735, 271932636847, 1146871941694, 4848125819247, 20538011410752, 87180357318349, 370753442344240, 1579383361624263, 6738572455070115

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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + 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: A084528 A149993 A148413 * A149995 A149996 A149997

Adjacent sequences: A149991 A149992 A149993 * A149995 A149996 A149997

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved