A148608 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, 0), (-1, 0, 1), (-1, 1, -1), (1, -1, -1), (1, 1, 0)}.

1, 1, 3, 6, 21, 53, 202, 569, 2281, 6933, 28501, 91572, 383287, 1281011, 5443007, 18740143, 80575328, 284058305, 1232785476, 4430127226, 19373902057, 70731957328, 311300116487, 1151847453464, 5096538704551, 19076836805680, 84795133135936, 320604977681090, 1430770492083279, 5457642756936573

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A148605 A148606 A148607 * A148609 A148610 A148611

Adjacent sequences: A148605 A148606 A148607 * A148609 A148610 A148611

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved