A150613 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, 0), (0, 1, 1), (1, 0, -1), (1, 0, 1)}.

1, 2, 7, 27, 112, 478, 2105, 9484, 43245, 199431, 929300, 4361745, 20586755, 97701197, 465803681, 2228618096, 10697330605, 51501214062, 248561101771, 1202215078663, 5826560923501, 28289465032495, 137566893876292, 669929533589892, 3266815957336537, 15949097240017185, 77950068718501772

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150610 A150611 A150612 * A150614 A182454 A192455

Adjacent sequences: A150610 A150611 A150612 * A150614 A150615 A150616

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved