A150507 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, -1, 1), (1, 0, 1), (1, 1, 0)}.

1, 2, 7, 25, 102, 418, 1822, 7930, 35834, 161326, 745277, 3428471, 16073766, 75051209, 355567823, 1678216641, 8012934452, 38128613404, 183143821040, 876997842618, 4232442545636, 20369705463788, 98680751392001, 476873322718406, 2317449590232091, 11236950192377100, 54750669538493457, 266229930746142702

Offset

0,2

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, 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, 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: A150504 A150505 A150506 * A150508 A150509 A150510

Adjacent sequences: A150504 A150505 A150506 * A150508 A150509 A150510

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved