A148632 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, 1, -1), (0, 0, 1), (1, 0, -1), (1, 1, -1)}.

1, 1, 3, 6, 22, 57, 199, 635, 2267, 7697, 28005, 102183, 376924, 1400719, 5332589, 20300989, 77782887, 301584310, 1177868933, 4605656965, 18140074145, 71985896850, 286147136610, 1141366553411, 4581599272046, 18440051763289, 74352815530058, 301118904892483, 1223523622764878, 4978403368998056

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A151264 A148630 A148631 * A148633 A148634 A323924

Adjacent sequences: A148629 A148630 A148631 * A148633 A148634 A148635

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved