A148559 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, 1, 0), (0, -1, 1), (1, 0, 0)}.

1, 1, 3, 6, 18, 47, 151, 460, 1525, 5038, 17053, 58515, 203966, 721558, 2574957, 9302325, 33775642, 123614239, 455228563, 1688097815, 6293391801, 23589993847, 88808957276, 335602754282, 1273156370290, 4847926721793, 18524640364142, 71012201291584, 273027194841206, 1052433038546206, 4066858704595868

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[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A148556 A148557 A148558 * A108507 A287212 A083337

Adjacent sequences: A148556 A148557 A148558 * A148560 A148561 A148562

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved