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

1,1

Links

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

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

Example

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

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

Crossrefs

Row 6 of A212402.

Sequence in context: A321533 A345157 A345126 * A190607 A256395 A182585

Adjacent sequences: A212404 A212405 A212406 * A212408 A212409 A212410

Keyword

nonn

Author

R. H. Hardin, May 14 2012

Status

approved