A148959 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, 0), (0, -1, 0), (0, 1, 1), (1, 1, -1)}.

1, 1, 3, 9, 31, 100, 370, 1372, 5290, 20266, 80361, 321735, 1307984, 5335667, 22024808, 91659114, 384509857, 1620023737, 6864307125, 29248903041, 125269708719, 538502958487, 2323193194405, 10060821504853, 43727466779310, 190618286246040, 833147784737097, 3651348013005285, 16045299842617819

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, k, -1 + n] + aux[1 + i, j, 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: A001672 A138281 A049416 * A148960 A027029 A027092

Adjacent sequences: A148956 A148957 A148958 * A148960 A148961 A148962

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved