cp's OEIS Frontend

A213121 Number of binary arrays of length 2*n+3 with fewer than n ones in any length 2n subsequence (=less than 50% duty cycle).

%I A213121 #12 Oct 29 2012 17:42:29
%S A213121 1,14,86,424,1926,8404,35836,150604,626726,2589844,10646676,43594464,
%T A213121 177950236,724578824,2944375096,11944652884,48388816486,195794585044,
%U A213121 791434666276,3196307541904,12898839944116,52019043912664
%N A213121 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 A213121 Row 4 of A213118.
%H A213121 R. H. Hardin, <a href="/A213121/b213121.txt">Table of n, a(n) for n = 1..210</a>
%F A213121 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 A213121 a(n) = 2^(2*n+2) - 5*(7*n-4)*C(2*n-2,n-1)/n. - _Vaclav Kotesovec_, Oct 29 2012
%e A213121 Some solutions for n=3
%e A213121 ..0....0....1....0....0....0....0....0....0....0....1....1....1....1....0....1
%e A213121 ..0....0....0....0....0....1....0....1....1....0....1....0....0....0....0....0
%e A213121 ..1....1....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A213121 ..0....0....0....1....0....0....0....1....0....1....0....0....0....0....0....1
%e A213121 ..1....0....1....0....1....1....0....0....1....1....0....0....0....0....0....0
%e A213121 ..0....0....0....0....1....0....0....0....0....0....0....0....1....0....0....0
%e A213121 ..0....0....0....0....0....0....0....0....0....0....1....0....0....1....0....0
%e A213121 ..0....1....0....1....0....0....0....0....0....0....0....1....1....0....1....0
%e A213121 ..0....1....1....0....0....1....0....0....0....0....0....1....0....0....1....0
%t A213121 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 A213121 nonn
%O A213121 1,2
%A A213121 _R. H. Hardin_, Jun 05 2012