A150470 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, 0)}.

1, 2, 7, 25, 98, 403, 1711, 7464, 33175, 149754, 684058, 3155132, 14669665, 68664134, 323240314, 1529158466, 7264937874, 34644069379, 165748338880, 795297442886, 3825885604124, 18447555311807, 89135166391835, 431494654085530, 2092386272672094, 10162065509008536, 49423947710676789, 240689237776366096

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[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: A150467 A150468 A150469 * A150471 A150472 A150473

Adjacent sequences: A150467 A150468 A150469 * A150471 A150472 A150473

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved