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%I #9 Jul 31 2013 06:36:42
%S 5,67,690,6681,63052,587036,5420945,49790907,455613780,4157731326,
%T 37863399867,344260235646,3126088840815,28357517641471,
%U 257019958093802,2327867460241673,21071246269530444,190634200830191606
%N Number of 0..2 arrays of length 2*n+1 with sum less than 2*n in any length 2n subsequence (=less than 50% duty cycle)
%C Row 2 of A212729
%H R. H. Hardin, <a href="/A212731/b212731.txt">Table of n, a(n) for n = 1..210</a>
%F From _Vaclav Kotesovec_, Jul 31 2013: (Start)
%F Empirical: n*(2*n-1)*(816*n^3 - 5572*n^2 + 11983*n - 8097)*a(n) = (31008*n^5 - 250088*n^4 + 727230*n^3 - 936367*n^2 + 518859*n - 93600)*a(n-1) - 9*(17952*n^5 - 157672*n^4 + 514566*n^3 - 767531*n^2 + 504861*n - 106650)*a(n-2) + 81*(n-3)*(2*n-5)*(816*n^3 - 3124*n^2 + 3287*n - 870)*a(n-3).
%F Conjecture: a(n) ~ 3/2*9^n. (End)
%e Some solutions for n=3
%e ..0....1....0....0....2....1....0....1....1....1....2....1....0....2....0....2
%e ..0....0....0....1....0....2....1....2....0....1....0....0....1....0....1....1
%e ..0....0....1....0....0....0....1....0....0....0....1....1....0....0....0....0
%e ..2....1....1....1....2....1....2....2....0....1....0....1....0....2....1....0
%e ..0....2....0....2....0....0....0....0....0....0....1....0....2....0....0....2
%e ..0....0....1....0....1....1....0....0....1....1....1....2....2....0....2....0
%e ..2....0....2....0....2....1....1....0....1....0....1....1....0....0....1....2
%K nonn
%O 1,1
%A _R. H. Hardin_ May 25 2012
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