%I #18 May 11 2019 02:21:24

%S 34,166,747,3179,13185,54042,220054,892387,3609005,14567294,58714842,

%T 236397086,950965002,3822869204,15359318444,61681353571,247609729669,

%U 993662549686,3986465243314,15989373858826,64118439206974

%N Number of binary arrays of length 2*n+5 with no more than n ones in any length 2n subsequence (=50% duty cycle).

%H R. H. Hardin, <a href="/A212407/b212407.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical (for n>=5): n*(181*n^2 - 792*n + 581)*a(n) = 2*(724*n^3 - 3711*n^2 + 4112*n + 210)*a(n-1) - 8*(2*n-7)*(181*n^2 - 430*n - 30)*a(n-2). - _Vaclav Kotesovec_, Nov 20 2012

%F Empirical (for n>=3): a(n) = 4^(n+2) - 2*(181*n^2 - 264*n - 6) * C(2*n - 5, n - 3) / (n*(n-1)). - _Vaclav Kotesovec_, Nov 20 2012

%e Some solutions for n=3:

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

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

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

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

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

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

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

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

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

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

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

%p #verified first terms (holds for all n<=210).

%p with(gfun): A212407:= rectoproc({a(3)=747, a(4)=3179, n*(181*n^2-792*n+581)*a(n) = 2*(724*n^3-3711*n^2+4112*n+210)*a(n-1) - 8*(2*n-7)*(181*n^2-430*n-30)*a(n-2)},a(n),remember): 34,166,seq(A212407(n),n=3..20); A212407(210); # _Vaclav Kotesovec_, Nov 20 2012

%Y Row 6 of A212402.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 14 2012