A148602 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), (0, 1, -1), (0, 1, 1), (1, -1, -1)}.

1, 1, 3, 6, 20, 58, 193, 632, 2283, 8009, 29503, 109608, 417840, 1593676, 6201714, 24352821, 96549718, 384965234, 1551154581, 6289703937, 25643105136, 105131398752, 433780213485, 1797589931543, 7479489370556, 31262568274435, 131224989229643, 552593121507505, 2334726454418711

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[i, -1 + j, -1 + k, -1 + n] + aux[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: A148599 A148600 A148601 * A148603 A185172 A173110

Adjacent sequences: A148599 A148600 A148601 * A148603 A148604 A148605

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved