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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
1, 26, 212, 1198, 5842, 26630, 116992, 502492, 2126238, 8903350, 36998056, 152862180, 628749892, 2576996188, 10531805664, 42940549576, 174734720374, 709858318486, 2879728611544, 11668224303796, 47228199967804 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 20 03:13 EDT 2019. Contains 328244 sequences. (Running on oeis4.)