A150384 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, 0, 1), (1, 0, 1), (1, 1, 0)}.

1, 2, 7, 23, 98, 361, 1593, 6288, 28328, 115850, 529887, 2219923, 10237960, 43662198, 202691642, 875687198, 4085356332, 17833779506, 83512309548, 367612178355, 1726842287851, 7653765309804, 36044855095680, 160691867249588, 758388273185977, 3397813146226703, 16065577291899227, 72289418439880710

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, -1 + j, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A150381 A150382 A150383 * A150385 A047066 A150386

Adjacent sequences: A150381 A150382 A150383 * A150385 A150386 A150387

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved