A148724 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, 0), (0, 1, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 7, 25, 71, 249, 847, 3029, 10683, 39689, 147239, 551221, 2092331, 8054273, 31025487, 120541229, 472911683, 1862132473, 7357610135, 29280001861, 117020171467, 468756101073, 1886067433695, 7620751816541, 30858228939091, 125300855281193, 510567657915239, 2085135808856565

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[1 + i, 1 + 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: A148721 A148722 A148723 * A332508 A309911 A148725

Adjacent sequences: A148721 A148722 A148723 * A148725 A148726 A148727

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved