A212731 - OEIS

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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 (list; graph; refs; listen; history; text; internal format)

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

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Last modified March 25 22:21 EDT 2023. Contains 361529 sequences. (Running on oeis4.)