A148486 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, 0, 0), (-1, 0, 1), (0, -1, 1), (0, 0, 1), (1, 1, -1)}.

1, 1, 2, 6, 21, 71, 260, 1000, 3953, 15917, 65410, 273438, 1157570, 4949533, 21375685, 93089976, 408147676, 1800678253, 7989131978, 35618243432, 159490955535, 717004472555, 3234915611753, 14642248373759, 66471250888687, 302578116535178, 1380765732673355, 6315304036774097, 28945896397033450

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A294702 A116785 A116801 * A294753 A294754 A116750

Adjacent sequences: A148483 A148484 A148485 * A148487 A148488 A148489

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved