A149734 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), (1, -1, 1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 75, 303, 1389, 6045, 28317, 127803, 606887, 2801619, 13424071, 62911801, 303379905, 1437067481, 6962892139, 33245183393, 161666164103, 776608858891, 3787408372649, 18281348949173, 89363341487161, 433014462826249, 2120749997875277, 10308769555144033, 50570373773643695, 246466322437473967

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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[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: A149731 A149732 A149733 * A149735 A149736 A145959

Adjacent sequences: A149731 A149732 A149733 * A149735 A149736 A149737

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved