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

1,2

Links

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

Example

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

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);

Crossrefs

Row 7 of A213118.

Sequence in context: A171586 A017594 A014800 * A067473 A223299 A068075

Adjacent sequences: A213121 A213122 A213123 * A213125 A213126 A213127

Keyword

nonn

Author

R. H. Hardin, Jun 05 2012

Status

approved