A150448 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), (1, 0, 0), (1, 1, -1), (1, 1, 0)}.

1, 2, 7, 24, 103, 416, 1902, 8283, 39070, 177344, 851579, 3965436, 19254227, 91187768, 446032075, 2137425882, 10508325562, 50787684839, 250604293372, 1218908813784, 6030763382894, 29475469821857, 146131936379380, 716924969782732, 3559893624198634, 17517194768320811, 87087929619336864

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[-1 + i, j, 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: A150445 A150446 A150447 * A256492 A150449 A150450

Adjacent sequences: A150445 A150446 A150447 * A150449 A150450 A150451

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved