A212406 Number of binary arrays of length 2*n+4 with no more than n ones in any length 2n subsequence (=50% duty cycle).

21, 97, 421, 1747, 7143, 29002, 117290, 473171, 1905675, 7665886, 30810054, 123745422, 496747206, 1993227892, 7995168852, 32060722883, 128532812627, 515187798518, 2064622548782, 8272744298618, 33143688036722, 132770436380108

Offset

1,1

Links

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

Formula

Empirical (for n>=4): n*(59*n^2 - 252*n + 163)*a(n) = 2*(236*n^3 - 1185*n^2 + 1204*n + 210)*a(n-1) - 8*(2*n-7)*(59*n^2 - 134*n - 30)*a(n-2). - Vaclav Kotesovec, Nov 20 2012

Empirical (for n>=3): a(n) = 2^(2*n+3) - 2*(59*n^2 - 84*n - 6) * C(2*n - 5, n - 3) / (n*(n-1)). - Vaclav Kotesovec, Nov 20 2012

Example

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

Maple

#verified first terms (holds for all n<=210).
with(gfun): A212406:= rectoproc({a(2)=97, a(3)=421, n*(59*n^2-252*n+163)*a(n) = 2*(236*n^3-1185*n^2+1204*n+210)*a(n-1) - 8*(2*n-7)*(59*n^2-134*n-30)*a(n-2)}, a(n), remember): 21, seq(A212406(n), n=2..20); A212406(210); # Vaclav Kotesovec, Nov 20 2012

Crossrefs

Row 5 of A212402.

Sequence in context: A220157 A264239 A200255 * A288750 A178794 A140370

Adjacent sequences: A212403 A212404 A212405 * A212407 A212408 A212409

Keyword

nonn

Author

R. H. Hardin, May 14 2012

Status

approved