A212407 Number of binary arrays of length 2*n+5 with no more than n ones in any length 2n subsequence (=50% duty cycle).

34, 166, 747, 3179, 13185, 54042, 220054, 892387, 3609005, 14567294, 58714842, 236397086, 950965002, 3822869204, 15359318444, 61681353571, 247609729669, 993662549686, 3986465243314, 15989373858826, 64118439206974

Offset: 1

Author

R. H. Hardin, May 14 2012

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 6 of A212402.

Programs

Maple

#verified first terms (holds for all n<=210).
with(gfun): A212407:= rectoproc({a(3)=747, a(4)=3179, n*(181*n^2-792*n+581)*a(n) = 2*(724*n^3-3711*n^2+4112*n+210)*a(n-1) - 8*(2*n-7)*(181*n^2-430*n-30)*a(n-2)},a(n),remember): 34,166,seq(A212407(n),n=3..20); A212407(210); # Vaclav Kotesovec, Nov 20 2012

Formula

Empirical (for n>=5): n*(181*n^2 - 792*n + 581)*a(n) = 2*(724*n^3 - 3711*n^2 + 4112*n + 210)*a(n-1) - 8*(2*n-7)*(181*n^2 - 430*n - 30)*a(n-2). - Vaclav Kotesovec, Nov 20 2012

Empirical (for n>=3): a(n) = 4^(n+2) - 2*(181*n^2 - 264*n - 6) * C(2*n - 5, n - 3) / (n*(n-1)). - Vaclav Kotesovec, Nov 20 2012