A149670 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, 0, 0), (0, 0, -1), (1, -1, 1), (1, 1, 1)}.

1, 1, 5, 17, 63, 259, 1067, 4441, 19171, 82665, 359847, 1592493, 7054023, 31408477, 141222211, 635735405, 2871906307, 13053172561, 59402203413, 271013152957, 1241586416665, 5694526128321, 26168463733923, 120610935005569, 556464506959781, 2571287472113759, 11907609696676003, 55193902622249547

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, 1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, 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: A149667 A149668 A149669 * A149671 A366978 A275220

Adjacent sequences: A149667 A149668 A149669 * A149671 A149672 A149673

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved