A213124 Number of binary arrays of length 2*n+6 with fewer than n ones in any length 2n subsequence (=less than 50% duty cycle).

1, 36, 324, 1996, 10154, 47448, 211888, 920744, 3930286, 16570608, 69240296, 287379592, 1186575444, 4879222736, 19997163520, 81735122832, 333327346838, 1356783786272, 5513802056888, 22376476701512, 90701190829388

Offset: 1

Author

R. H. Hardin, Jun 05 2012

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 7 of A213118.

Programs

Maple

#verified first terms (holds for all n<=210). - Vaclav Kotesovec, Nov 20 2012
with(gfun): A213124:= rectoproc({a(3)=324, a(4)=1996, n*(143*n^3-1584*n^2+5761*n-6880)*a(n) = 2*(572*n^4-6765*n^3+27961*n^2-46078*n+23040)*a(n-1) - 8*(2*n-9)*(143*n^3-1155*n^2+3022*n-2560)*a(n-2)},a(n),remember): 1,36,seq(A213124(n),n=3..20); A213124(210);

Formula

Empirical (for n>=5): n*(143*n^3 - 1584*n^2 + 5761*n - 6880)*a(n) = 2*(572*n^4 - 6765*n^3 + 27961*n^2 - 46078*n + 23040)*a(n-1) - 8*(2*n-9)*(143*n^3 - 1155*n^2 + 3022*n - 2560)*a(n-2). - Vaclav Kotesovec, Nov 20 2012

Empirical (for n>=4): a(n) = 2^(2*n+5) - 12*(1001*n^3 - 4697*n^2 + 6510*n - 2560) * C(2*n-7, n-4) / ((n-2)*(n-1)*n). - Vaclav Kotesovec, Nov 20 2012