A148655 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, 0), (-1, 0, -1), (0, 1, 1), (1, -1, -1), (1, -1, 1)}

1, 1, 3, 6, 24, 64, 234, 773, 2834, 9831, 36850, 136350, 513560, 1943118, 7518616, 28941609, 112624730, 442163143, 1745001882, 6898346029, 27491740152, 109998293464, 441017760936, 1775880590304, 7183972818702, 29116762856767, 118326172979525, 482587819602284, 1972390878751295

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[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A148652 A148653 A148654 * A148656 A279300 A054718

Adjacent sequences: A148652 A148653 A148654 * A148656 A148657 A148658

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved