A148533 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, 0), (-1, 1, -1), (-1, 1, 1), (1, 0, 0)}.

1, 1, 3, 5, 19, 39, 165, 377, 1703, 4163, 19381, 49477, 234493, 617473, 2959003, 7974541, 38523859, 105732111, 513864265, 1431231201, 6988798153, 19703019965, 96571223019, 275040849031, 1352124052435, 3884420054879, 19142720376195, 55405212387287, 273587352809983, 797001922601467, 3942058763183233

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A148530 A148531 A148532 * A242818 A218373 A034511

Adjacent sequences: A148530 A148531 A148532 * A148534 A148535 A148536

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved