A148728 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, 1, 1), (0, 1, -1), (0, 1, 1), (1, 0, -1)}.

1, 1, 3, 7, 25, 72, 278, 918, 3678, 13040, 53884, 200694, 845723, 3266873, 13972607, 55450557, 240031808, 972983451, 4251703434, 17532731134, 77217505713, 322913991532, 1431620492774, 6057640157681, 27007621918993, 115423839180006, 517127199750207, 2229091048295270, 10029555035534357

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, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A148725 A148726 A148727 * A148729 A143339 A148730

Adjacent sequences: A148725 A148726 A148727 * A148729 A148730 A148731

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved