A212408 Number of binary arrays of length 2*n+6 with no more than n ones in any length 2n subsequence (=50% duty cycle).

55, 285, 1314, 5769, 24322, 100736, 413220, 1685039, 6844362, 27724036, 112072540, 452348578, 1823583124, 7344493104, 29556979016, 118871913787, 477820811258, 1919788147772, 7710323488748, 30956089143902, 124248950086268

Offset: 1

Author

R. H. Hardin, May 14 2012

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 7 of A212402.

Programs

Maple

#verified first terms (holds for all n<=210).
with(gfun): A212408:= rectoproc({a(3)=1314, a(4)=5769, n*(955*n^3-8481*n^2+21998*n-14262)*a(n) = 2*(3820*n^4-36789*n^3+110342*n^2-99213*n-1890)*a(n-1) - 8*(2*n-9)*(955*n^3-5616*n^2+7901*n+210)*a(n-2)},a(n),remember): 55,285,seq(A212408(n),n=3..20); A212408(210); # Vaclav Kotesovec, Nov 20 2012

Formula

Empirical (for n>=5): n*(955*n^3 - 8481*n^2 + 21998*n - 14262)*a(n) = 2*(3820*n^4 - 36789*n^3 + 110342*n^2 - 99213*n - 1890)*a(n-1) - 8*(2*n-9)*(955*n^3 - 5616*n^2 + 7901*n + 210)*a(n-2). - Vaclav Kotesovec, Nov 20 2012

Empirical (for n>=4): a(n) = 2^(2*n+5) - 4*(955*n^3 - 3782*n^2 + 3475*n + 30) * C(2*n-7, n-4) / ((n-2)*(n-1)*n). - Vaclav Kotesovec, Nov 20 2012