A212732 Number of 0..2 arrays of length 2*n+2 with sum less than 2*n in any length 2n subsequence (=less than 50% duty cycle)

8, 148, 1669, 16878, 163495, 1549297, 14492156, 134429604, 1239807015, 11386939467, 104257566078, 952281922551, 8681609266794, 79026329849968, 718456060049941, 6524950672498742, 59207190970359999, 536844632687526915

Offset

1,1

Comments

Row 3 of A212729

Links

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

Formula

From Vaclav Kotesovec, Jul 31 2013: (Start)

Empirical: n*(2*n-1)*(59040*n^4 - 630664*n^3 + 2419338*n^2 - 3925427*n + 2259783)*a(n) = (2243520*n^6 - 26740112*n^5 + 122386084*n^4 - 271040464*n^3 + 300314759*n^2 - 153351297*n + 26751060)*a(n-1) + 81*(n-3)*(2*n-7)*(59040*n^4 - 394504*n^3 + 881586*n^2 - 742583*n + 182070)*a(n-3) - 9*(1298880*n^6 - 16413328*n^5 + 81293588*n^4 - 199839104*n^3 + 252840847*n^2 - 150974403*n + 30574530)*a(n-2)

Conjecture: a(n) ~ 9/2*9^n. (End)

Example

Some solutions for n=3
..2....0....1....1....2....0....0....0....0....1....0....1....1....0....1....0
..0....0....0....0....0....1....0....0....1....1....2....0....0....1....0....2
..0....1....1....0....0....0....1....2....1....0....0....1....0....1....0....1
..2....2....1....2....1....1....0....1....0....1....1....0....0....0....0....0
..0....1....0....0....1....0....1....0....0....1....0....1....2....0....0....0
..0....0....0....0....0....2....0....0....0....0....1....1....0....1....0....0
..0....1....1....1....2....0....0....0....1....0....0....0....0....2....0....2
..2....0....1....0....0....2....2....1....1....2....0....2....1....0....0....1

Crossrefs

Sequence in context: A239759 A279127 A259991 * A220297 A307942 A116876

Adjacent sequences: A212729 A212730 A212731 * A212733 A212734 A212735

Keyword

nonn

Author

R. H. Hardin May 25 2012

Status

approved