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%I #17 May 11 2019 02:21:17
%S 21,97,421,1747,7143,29002,117290,473171,1905675,7665886,30810054,
%T 123745422,496747206,1993227892,7995168852,32060722883,128532812627,
%U 515187798518,2064622548782,8272744298618,33143688036722,132770436380108
%N Number of binary arrays of length 2*n+4 with no more than n ones in any length 2n subsequence (=50% duty cycle).
%H R. H. Hardin, <a href="/A212406/b212406.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical (for n>=4): n*(59*n^2 - 252*n + 163)*a(n) = 2*(236*n^3 - 1185*n^2 + 1204*n + 210)*a(n-1) - 8*(2*n-7)*(59*n^2 - 134*n - 30)*a(n-2). - _Vaclav Kotesovec_, Nov 20 2012
%F Empirical (for n>=3): a(n) = 2^(2*n+3) - 2*(59*n^2 - 84*n - 6) * C(2*n - 5, n - 3) / (n*(n-1)). - _Vaclav Kotesovec_, Nov 20 2012
%e Some solutions for n=3:
%e 0 1 1 0 0 0 1 0 0 0 1 0 1 0 0 1
%e 1 0 0 0 1 0 1 0 1 1 1 0 1 1 1 0
%e 1 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0
%e 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1
%e 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1
%e 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0
%e 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0
%e 1 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1
%e 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0
%e 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1
%p #verified first terms (holds for all n<=210).
%p with(gfun): A212406:= rectoproc({a(2)=97, a(3)=421, n*(59*n^2-252*n+163)*a(n) = 2*(236*n^3-1185*n^2+1204*n+210)*a(n-1) - 8*(2*n-7)*(59*n^2-134*n-30)*a(n-2)},a(n),remember): 21,seq(A212406(n),n=2..20); A212406(210); # _Vaclav Kotesovec_, Nov 20 2012
%Y Row 5 of A212402.
%K nonn
%O 1,1
%A _R. H. Hardin_, May 14 2012
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