A210543 Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 6 times.

1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 64, 129, 267, 582, 1364, 3454, 9338, 26429, 76929, 227579, 680113, 2050000, 6242818, 19284165, 60754153, 196341570, 654012814, 2251195713, 8005274899, 29325473071, 110181281435, 422565983725

Offset

1,7

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

a(n) = 1 if n<=6 else Sum_{i=0..n-6} (binomial(n-6,i)*a(i)).

Example

Some solutions for n=17
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....1....1....1....0....0....1....1....1....0....1....1....1....1....0....0
..1....0....0....1....0....1....1....1....1....1....0....1....0....1....1....1
..0....0....0....1....1....1....1....0....1....1....1....0....1....1....1....1
..1....1....1....0....0....1....0....1....1....1....1....0....1....0....1....1
..0....0....1....1....0....1....1....1....0....0....0....0....0....1....1....1
..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....0
..0....1....0....0....1....0....0....1....1....1....1....1....1....1....1....0
..1....1....0....1....0....1....0....1....2....1....1....1....1....0....0....1
..1....0....0....1....1....0....1....0....2....1....0....0....0....0....1....1
..1....0....1....1....0....0....2....1....0....1....0....0....0....0....1....1
..2....0....1....0....1....0....1....1....2....0....0....1....2....1....2....0

Crossrefs

Column 6 of A210545.

Sequence in context: A023422 A084638 A157021 * A006211 A180209 A344493

Adjacent sequences: A210540 A210541 A210542 * A210544 A210545 A210546

Keyword

nonn

Author

R. H. Hardin, formula proved by R. J. Mathar in the Sequence Fans Mailing List, Mar 22 2012

Status

approved