A150585 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, 1), (0, 0, 1), (1, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 26, 110, 471, 2119, 9586, 44409, 206599, 973748, 4604843, 21946347, 104877487, 503695712, 2424445881, 11709284723, 56654824221, 274788262853, 1334791475699, 6495565211266, 31649525489011, 154428850634500, 754311477162251, 3688596553559261, 18053599261036996, 88443596719419751

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, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A150582 A150583 A150584 * A150586 A196709 A150587

Adjacent sequences: A150582 A150583 A150584 * A150586 A150587 A150588

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved