A210544 Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 7 times

1, 1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 64, 128, 257, 524, 1106, 2470, 5924, 15262, 41690, 118595, 345861, 1023028, 3050590, 9146312, 27567958, 83678750, 256632743, 798853376, 2537255097, 8264988956, 27723246374, 95941707086, 342355797248

Offset

1,8

Comments

Column 7 of A210545

Links

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

Formula

a(n) = 1 if n<=7 else sum{i=0..n-7}(binomial(n-7,i)*a(i))

Example

Some solutions for n=19
..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....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....1....1....0....1....1....0....1....1....1....1....0....1....0....0....0
..1....1....0....0....0....1....1....0....0....1....1....1....0....1....1....1
..1....0....1....1....1....0....1....0....0....1....0....0....0....1....0....1
..0....1....0....0....0....1....1....0....1....1....1....1....0....1....1....1
..0....0....1....0....1....0....1....0....1....0....1....0....0....1....1....0
..1....0....0....1....1....1....0....0....0....1....1....0....1....1....1....0
..0....1....1....0....1....1....0....0....0....1....1....1....0....1....1....0
..0....1....1....0....1....1....0....0....1....0....1....0....0....1....1....1
..1....1....1....1....0....1....0....0....1....1....2....1....1....0....1....0
..1....1....1....1....0....2....0....0....0....1....1....1....1....0....2....1
..0....0....1....1....1....1....0....0....1....0....1....1....0....1....2....1
..0....1....1....1....0....2....1....1....1....0....0....0....1....1....2....1

Crossrefs

Sequence in context: A186026 A367653 A023423 * A180210 A274861 A290666

Adjacent sequences: A210541 A210542 A210543 * A210545 A210546 A210547

Keyword

nonn

Author

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

Status

approved