A150988 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, 0, 0), (0, -1, 1), (1, 0, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 37, 165, 746, 3448, 16119, 76013, 361046, 1723957, 8267905, 39795471, 192115078, 929836921, 4510146186, 21918059442, 106692274128, 520116707988, 2538844379366, 12407352640571, 60698913755434, 297233707139452, 1456780194366246, 7145567035991768, 35075029494865320, 172287382987613178

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150985 A150986 A150987 * A150989 A150990 A150991

Adjacent sequences: A150985 A150986 A150987 * A150989 A150990 A150991

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved