A148669 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), (1, 0, 1)}

1, 1, 3, 7, 19, 60, 185, 571, 1857, 6100, 20193, 68372, 233154, 795296, 2743437, 9550939, 33338093, 116943668, 412645815, 1460122884, 5181607406, 18468520608, 66016250037, 236455799708, 849337831838, 3058593825728, 11033836131750, 39881355285040, 144452154327412, 524058450659536, 1904071884603245

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, 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: A201169 A148667 A148668 * A249380 A364626 A210985

Adjacent sequences: A148666 A148667 A148668 * A148670 A148671 A148672

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved