A212734 Number of 0..2 arrays of length 2*n+4 with sum less than 2*n in any length 2n subsequence (=less than 50% duty cycle).

21, 677, 9807, 109995, 1128418, 11095332, 106521624, 1007510947, 9434164257, 87714102222, 811255784844, 7473287004534, 68629364053569, 628674775710013, 5747280092974905, 52453265961232251, 478052219263361986

Offset

1,1

Comments

Row 5 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)*(13283136*n^6 - 264953520*n^5 + 2147785772*n^4 - 9019996352*n^3 + 20594052913*n^2 - 24090888493*n + 11202753384)*a(n) = (504759168*n^8 - 10692541152*n^7 + 94303861048*n^6 - 448109760340*n^5 + 1240039075502*n^4 - 2015761359053*n^3 + 1843073445627*n^2 - 843009243120*n + 141051002400)*a(n-1) - 9*(292228992*n^8 - 6400152288*n^7 + 58931188760*n^6 - 296092883492*n^5 + 880725021838*n^4 - 1570768747177*n^3 + 1613191469925*n^2 - 846280196028*n + 162004328640)*a(n-2) + 81*(n-4)*(2*n-9)*(13283136*n^6 - 185254704*n^5 + 1022265212*n^4 - 2812725744*n^3 + 3970490329*n^2 - 2616697419*n + 582036840)*a(n-3)

Conjecture: a(n) ~ 81/2*9^n. (End)

Example

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

Crossrefs

Sequence in context: A239099 A006934 A211877 * A339119 A243746 A276021

Adjacent sequences: A212731 A212732 A212733 * A212735 A212736 A212737

Keyword

nonn

Author

R. H. Hardin, May 25 2012

Status

approved