A150223 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), (0, 1, 0), (1, 0, -1), (1, 0, 1)}.

1, 2, 6, 21, 84, 341, 1445, 6309, 27788, 125044, 570195, 2614993, 12120861, 56615783, 265431493, 1252372891, 5937958979, 28227542252, 134746021085, 645350756373, 3096830635056, 14903561941625, 71893392943530, 347324211311272, 1681464054920885, 8154591774594199, 39593850266494760, 192545631945019300

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 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: A087649 A328435 A150222 * A150224 A150225 A123922

Adjacent sequences: A150220 A150221 A150222 * A150224 A150225 A150226

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved