A150106 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, 0, 0), (0, 0, 1), (0, 1, 1), (1, 0, -1)}.

1, 2, 6, 19, 69, 258, 1009, 4051, 16620, 69339, 293485, 1255837, 5427580, 23650266, 103780197, 458260421, 2034519989, 9075959960, 40663040317, 182882049074, 825372922736, 3736795149850, 16966383950246, 77235724826460, 352445379796634, 1611854862549043, 7386683542925906, 33915357128568520

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, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A145868 A058122 A150105 * A150107 A148472 A150108

Adjacent sequences: A150103 A150104 A150105 * A150107 A150108 A150109

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved