A150995 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), (0, 1, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 38, 171, 796, 3749, 17905, 86307, 418396, 2039335, 9978881, 48974426, 240998345, 1188333118, 5869632445, 29035136474, 143800709201, 712944995081, 3537872814069, 17569705426963, 87313570041560, 434165782813249, 2160005578393606, 10751118587912161, 53533873989477849, 266661692159814558

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[i, -1 + 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: A001077 A150993 A150994 * A150996 A150997 A150998

Adjacent sequences: A150992 A150993 A150994 * A150996 A150997 A150998

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved