A212731 Number of 0..2 arrays of length 2*n+1 with sum less than 2*n in any length 2n subsequence (=less than 50% duty cycle)

5, 67, 690, 6681, 63052, 587036, 5420945, 49790907, 455613780, 4157731326, 37863399867, 344260235646, 3126088840815, 28357517641471, 257019958093802, 2327867460241673, 21071246269530444, 190634200830191606

Offset

1,1

Comments

Row 2 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)*(816*n^3 - 5572*n^2 + 11983*n - 8097)*a(n) = (31008*n^5 - 250088*n^4 + 727230*n^3 - 936367*n^2 + 518859*n - 93600)*a(n-1) - 9*(17952*n^5 - 157672*n^4 + 514566*n^3 - 767531*n^2 + 504861*n - 106650)*a(n-2) + 81*(n-3)*(2*n-5)*(816*n^3 - 3124*n^2 + 3287*n - 870)*a(n-3).

Conjecture: a(n) ~ 3/2*9^n. (End)

Example

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

Crossrefs

Sequence in context: A226412 A226343 A067393 * A316146 A113265 A124435

Adjacent sequences: A212728 A212729 A212730 * A212732 A212733 A212734

Keyword

nonn

Author

R. H. Hardin May 25 2012

Status

approved