A148498 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, 0, 1), (-1, 1, 0), (1, 0, 0)}.

1, 1, 3, 5, 15, 29, 97, 209, 739, 1697, 6021, 14299, 52027, 127633, 473223, 1189853, 4416111, 11271917, 42295113, 109669063, 415390879, 1091329437, 4135009859, 10957215225, 41769771825, 111723881139, 428304396077, 1155044333999, 4428390412119, 12008999091781, 46220639036797, 126123622938745

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 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: A048738 A018454 A126087 * A259921 A292689 A286521

Adjacent sequences: A148495 A148496 A148497 * A148499 A148500 A148501

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved