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

Author

R. H. Hardin, May 14 2012

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Row 5 of A212402.

Programs

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

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