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

1,1

Links

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

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

Example

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

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

Crossrefs

Row 7 of A212402.

Sequence in context: A286854 A020182 A159746 * A350286 A250092 A330382

Adjacent sequences: A212405 A212406 A212407 * A212409 A212410 A212411

Keyword

nonn

Author

R. H. Hardin, May 14 2012

Status

approved