A212405 Number of binary arrays of length 2*n+3 with no more than n ones in any length 2n subsequence (=50% duty cycle).

13, 57, 236, 959, 3872, 15586, 62632, 251419, 1008536, 4043582, 16206152, 64933782, 260114976, 1041797124, 4171943056, 16704821779, 66880877896, 267747443494, 1071808583176, 4290243456514, 17172082337536, 68729504287324

Offset: 1

Author

R. H. Hardin May 14 2012

Keywords

• nonn

Comments

Row 4 of A212402

Examples

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

Links

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

Programs

Mathematica

Flatten[{13,Table[2^(2*n+2)-(3*n+1)/n*Binomial[2*n-2,n-1],{n,2,20}]}] (* Vaclav Kotesovec, Oct 28 2012 *)

Formula

Recurrence (for n>3): n^2*a(n) = 2*(4*n^2-3*n-5)*a(n-1) - 8*(n+1)*(2*n-5)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

a(n) = 2^(2*n+2) - (3*n+1)/n * C(2*n-2,n-1), for n>1. - Vaclav Kotesovec, Oct 28 2012