A148565 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, 0, 1), (0, 1, -1), (1, 0, -1)}.

1, 1, 3, 6, 18, 51, 168, 549, 1909, 6683, 24229, 89289, 335672, 1277955, 4928340, 19227809, 75796636, 301563679, 1209229277, 4885143469, 19868156821, 81315289674, 334668089608, 1384559863050, 5755539035995, 24033260799961, 100773058097799, 424183379687942, 1791954886891733

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, j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A148562 A148563 A148564 * A112572 A089325 A110593

Adjacent sequences: A148562 A148563 A148564 * A148566 A148567 A148568

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved