A212733 Number of 0..2 arrays of length 2*n+3 with sum less than 2*n in any length 2n subsequence (=less than 50% duty cycle)

13, 322, 4057, 43050, 428617, 4135249, 39179582, 366956550, 3410099667, 31512792243, 290000751576, 2660274782385, 24342553658646, 222296998969810, 2026699958947573, 18452534543569730, 167814036979752705

Offset

1,1

Comments

Row 4 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)*(641952*n^5 - 9661256*n^4 + 56355290*n^3 - 158324563*n^2 + 212843323*n - 108787536)*a(n) = (24394176*n^7 - 397299472*n^6 + 2605594692*n^5 - 8806725568*n^4 + 16309249503*n^3 - 16218569485*n^2 + 7794486684*n - 1330045920)*a(n-1) - 9*(14122944*n^7 - 240151568*n^6 + 1667254836*n^5 - 6073887920*n^4 + 12400532871*n^3 - 13948629407*n^2 + 7754485194*n - 1524164040)*a(n-2) + 81*(n-4)*(2*n-7)*(641952*n^5 - 6451496*n^4 + 24129786*n^3 - 40806709*n^2 + 29824803*n - 6932790)*a(n-3)

Conjecture: a(n) ~ 27/2*9^n. (End)

Example

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

Crossrefs

Sequence in context: A132485 A297437 A166743 * A183803 A253458 A012492

Adjacent sequences: A212730 A212731 A212732 * A212734 A212735 A212736

Keyword

nonn

Author

R. H. Hardin May 25 2012

Status

approved