A149500 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, -1, 1), (-1, 0, -1), (0, -1, -1), (1, 1, 1)}.

1, 1, 5, 9, 45, 121, 509, 1745, 6565, 25473, 95333, 377369, 1466925, 5767385, 23131709, 91583241, 369636245, 1489745457, 6019414749, 24561243097, 99915769557, 409006211521, 1680181737581, 6897520420113, 28491147830797, 117644375606081, 486929303998637, 2022669691473049, 8395994639957741

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, -1 + j, -1 + k, -1 + n] + aux[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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A149498 A149499 A100305 * A149501 A149502 A219701

Adjacent sequences: A149497 A149498 A149499 * A149501 A149502 A149503

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved