A148507 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), (-1, 0, 1), (-1, 1, -1), (1, 0, 0)}.

1, 1, 3, 5, 17, 34, 126, 279, 1095, 2588, 10568, 26135, 109831, 280825, 1206019, 3163573, 13817947, 36988956, 163766640, 445663467, 1995178007, 5504179695, 24870604773, 69405571235, 316074230017, 890773057954, 4083914536666, 11607708438209, 53528079869585, 153276618466706, 710428433436742, 2047649064421003

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, 1 + k, -1 + n] + aux[1 + 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: A148504 A148505 A148506 * A148508 A148509 A148510

Adjacent sequences: A148504 A148505 A148506 * A148508 A148509 A148510

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved