A150510 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, 0, 1), (0, 0, 1), (0, 1, -1), (0, 1, 1), (1, -1, 1)}.

1, 2, 7, 25, 102, 421, 1833, 8055, 36333, 165105, 761383, 3531580, 16531186, 77736848, 367792638, 1746466460, 8329088373, 39838754439, 191165146280, 919486724021, 4433590609255, 21419834806102, 103687748482389, 502743056244639, 2441491903750180, 11872958808117098, 57814141613740897, 281847208285495504

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, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A150507 A150508 A150509 * A150511 A036784 A221456

Adjacent sequences: A150507 A150508 A150509 * A150511 A150512 A150513

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved