A150610 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, 0, 1), (1, 1, -1), (1, 1, 0)}.

1, 2, 7, 27, 111, 476, 2099, 9450, 43187, 199718, 932105, 4382967, 20735681, 98601676, 470881455, 2256986579, 10852089299, 52322169006, 252870073029, 1224688067121, 5942461675845, 28882364388668, 140588554044485, 685257943984676, 3344181251535477, 16338385098193602, 79904287114428487

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, 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: A150607 A150608 A150609 * A150611 A150612 A150613

Adjacent sequences: A150607 A150608 A150609 * A150611 A150612 A150613

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved