A213121 - OEIS

%I #12 Oct 29 2012 17:42:29

%S 1,14,86,424,1926,8404,35836,150604,626726,2589844,10646676,43594464,

%T 177950236,724578824,2944375096,11944652884,48388816486,195794585044,

%U 791434666276,3196307541904,12898839944116,52019043912664

%N Number of binary arrays of length 2*n+3 with fewer than n ones in any length 2n subsequence (=less than 50% duty cycle).

%C Row 4 of A213118.

%H R. H. Hardin, <a href="/A213121/b213121.txt">Table of n, a(n) for n = 1..210</a>

%F Recurrence: n*(7*n-19)*a(n) = 2*(28*n^2-97*n+60)*a(n-1) - 8*(2*n-5)*(7*n-12) * a(n-2). - _Vaclav Kotesovec_, Oct 19 2012

%F a(n) = 2^(2*n+2) - 5*(7*n-4)*C(2*n-2,n-1)/n. - _Vaclav Kotesovec_, Oct 29 2012

%e Some solutions for n=3

%e ..0....0....1....0....0....0....0....0....0....0....1....1....1....1....0....1

%e ..0....0....0....0....0....1....0....1....1....0....1....0....0....0....0....0

%e ..1....1....0....0....0....0....0....0....0....0....0....0....0....0....0....0

%e ..0....0....0....1....0....0....0....1....0....1....0....0....0....0....0....1

%e ..1....0....1....0....1....1....0....0....1....1....0....0....0....0....0....0

%e ..0....0....0....0....1....0....0....0....0....0....0....0....1....0....0....0

%e ..0....0....0....0....0....0....0....0....0....0....1....0....0....1....0....0

%e ..0....1....0....1....0....0....0....0....0....0....0....1....1....0....1....0

%e ..0....1....1....0....0....1....0....0....0....0....0....1....0....0....1....0

%t Table[2^(2*n+2)-5*(7*n-4)*Binomial[2*n-2,n-1]/n,{n,1,20}] (* _Vaclav Kotesovec_, Oct 29 2012 *)

%K nonn

%O 1,2

%A _R. H. Hardin_, Jun 05 2012