A212403 Number of binary arrays of length 2*n+1 with no more than n ones in any length 2n subsequence (=50% duty cycle).

5, 19, 74, 291, 1150, 4558, 18100, 71971, 286454, 1140954, 4547020, 18129294, 72309164, 288493756, 1151300584, 4595507491, 18346672294, 73257044386, 292550538844, 1168434892186, 4667175448324, 18644235526276, 74485459541464

Offset

1,1

Comments

Row 2 of A212402.

Links

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

Formula

Recurrence: n*a(n) = 2*(4*n-3)*a(n-1) - 8*(2*n-3)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

G.f.: 1/(1-4*x)+1/(2*sqrt(1-4*x)). - Vaclav Kotesovec, Oct 21 2012

a(n) = 4^n + C(2*n-1, n). - Vaclav Kotesovec, Oct 28 2012

Example

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

Mathematica

Rest[CoefficientList[Series[1/(1-4*x)+1/(2*Sqrt[1-4*x]), {x, 0, 20}], x]] (* Vaclav Kotesovec, Oct 21 2012 *)
Table[4^n + Binomial[2*n-1, n], {n, 1, 20}] (* Vaclav Kotesovec, Oct 28 2012 *)

Crossrefs

Sequence in context: A149766 A254686 A295374 * A098913 A126392 A206373

Adjacent sequences: A212400 A212401 A212402 * A212404 A212405 A212406

Keyword

nonn

Author

R. H. Hardin, May 14 2012

Status

approved