A148198 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), (0, 1, 0), (1, -1, 0), (1, 0, -1)}.

1, 1, 2, 4, 12, 33, 108, 360, 1259, 4495, 16726, 63085, 243465, 956363, 3809943, 15373894, 62802682, 259047003, 1078374062, 4527106194, 19143470222, 81500734973, 349136767609, 1504001293329, 6512451517597, 28334377206645, 123816571698718, 543263369796293, 2392666109152600, 10574852319611663

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[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: A231356 A148196 A148197 * A148199 A343663 A377101

Adjacent sequences: A148195 A148196 A148197 * A148199 A148200 A148201

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved