A150834 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), (0, 1, -1), (1, 0, -1), (1, 1, 0), (1, 1, 1)}.

1, 2, 8, 32, 136, 598, 2690, 12346, 57208, 267850, 1263588, 5994932, 28592366, 136903040, 657880056, 3170624544, 15320492804, 74194979122, 360020846672, 1750021243110, 8519797874060, 41535703432116, 202748248659314, 990797539945466, 4846864095569712, 23732581429494054, 116306501561327282

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + 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: A150832 A150833 A198760 * A150835 A150836 A150837

Adjacent sequences: A150831 A150832 A150833 * A150835 A150836 A150837

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved