A213120 Number of binary arrays of length 2*n+2 with fewer than n ones in any length 2n subsequence (=less than 50% duty cycle).

1, 10, 54, 252, 1110, 4748, 19964, 83024, 342678, 1406748, 5751636, 23443240, 95319484, 386805112, 1567130168, 6340730552, 25626393878, 103472018492, 417449893988, 1682982404072, 6780908053268, 27306234108392, 109907864408648

Offset: 1

Author

R. H. Hardin Jun 05 2012

Keywords

• nonn

Comments

Row 3 of A213118.

Examples

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

Links

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

Programs

Mathematica

Table[2^(2*n+1)-(15*n-8)*Binomial[2*n-2,n-1]/n,{n,1,20}] (* Vaclav Kotesovec, Oct 29 2012 *)

Formula

Recurrence: n*(5*n-13)*a(n) = 2*(20*n^2-67*n+40)*a(n-1) - 8*(2*n-5)*(5*n-8) * a(n-2). - Vaclav Kotesovec, Oct 19 2012

a(n) = 2^(2*n+1) - (15*n-8)*C(2*n-2,n-1)/n. - Vaclav Kotesovec, Oct 29 2012