A213123 Number of binary arrays of length 2*n+5 with fewer than n ones in any length 2n subsequence (=less than 50% duty cycle).

1, 26, 212, 1198, 5842, 26630, 116992, 502492, 2126238, 8903350, 36998056, 152862180, 628749892, 2576996188, 10531805664, 42940549576, 174734720374, 709858318486, 2879728611544, 11668224303796, 47228199967804

Offset

1,2

Links

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

Formula

Empirical (for n>=5): n*(33*n^2 - 213*n + 340)*a(n) = 2*(132*n^3 - 951*n^2 + 2029*n - 1120)*a(n-1) - 8*(2*n-7)*(33*n^2 - 147*n + 160)*a(n-2). - Vaclav Kotesovec, Nov 20 2012

Empirical (for n>=3): a(n) = 4^(n+2) - 42*(33*n^2 - 71*n + 32) * C(2*n - 5, n - 3) / ((n-1)*n). - Vaclav Kotesovec, Nov 20 2012

Example

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

Maple

#verified first terms (holds for all n<=210).
with(gfun): A213123:= rectoproc({a(3)=212, a(4)=1198, n*(33*n^2-213*n+340)*a(n) = 2*(132*n^3-951*n^2+2029*n-1120)*a(n-1) - 8*(2*n-7)*(33*n^2-147*n+160)*a(n-2)}, a(n), remember): 1, 26, seq(A213123(n), n=3..20); A213123(210); # Vaclav Kotesovec, Nov 20 2012

Crossrefs

Row 6 of A213118.

Sequence in context: A159762 A100242 A042310 * A125363 A126521 A242262

Adjacent sequences: A213120 A213121 A213122 * A213124 A213125 A213126

Keyword

nonn

Author

R. H. Hardin, Jun 05 2012

Status

approved