A150582 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), (-1, 0, 1), (0, 1, 1), (1, -1, 1), (1, 1, 0)}.

1, 2, 7, 26, 110, 462, 2032, 9032, 40840, 186321, 858818, 3984862, 18611847, 87360315, 411863886, 1949125972, 9255386301, 44077033173, 210463673995, 1007317519604, 4831514778409, 23218739899746, 111777775662186, 538973114127768, 2602666395019549, 12585155449922908, 60931611563543349

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A093638 A150580 A150581 * A150583 A150584 A150585

Adjacent sequences: A150579 A150580 A150581 * A150583 A150584 A150585

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved