A150943 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, 0, 1), (1, 0, -1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 34, 159, 686, 3295, 14981, 72979, 341250, 1675508, 7971231, 39327083, 189258001, 936712081, 4544151795, 22541054385, 109990199579, 546487806524, 2678303694963, 13323363269344, 65516973280506, 326220694997496, 1608413697594238, 8014380398790047, 39597817311750800, 197420514122489922

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[1 + i, 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: A150940 A150941 A150942 * A150944 A276901 A151308

Adjacent sequences: A150940 A150941 A150942 * A150944 A150945 A150946

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved