%I
%S 3,31,294,2727,25048,228826,2083371,18925047,171633840,1554702516,
%T 14069962041,127240600050,1150026301089,10389276050527,93819553163854,
%U 846952848390039,7643713441711560,68967751709641564,622154460094492809
%N Number of 0..2 arrays of length 2*n with sum less than 2*n in any length 2n subsequence (=less than 50% duty cycle)
%C Row 1 of A212729
%H R. H. Hardin, <a href="/A212730/b212730.txt">Table of n, a(n) for n = 1..210</a>
%F From _Vaclav Kotesovec_, Jul 31 2013: (Start)
%F Empirical: n*(2*n1)*(16*n^2  60*n + 53)*a(n) = (608*n^4  3032*n^3 + 5050*n^2  3259*n + 660)*a(n1)  9*(352*n^4  2008*n^3 + 3986*n^2  3143*n + 750)*a(n2) + 81*(n2)*(2*n5)*(16*n^2  28*n + 9)*a(n3).
%F Conjecture: a(n) ~ 9^n/2. (End)
%e Some solutions for n=3
%e ..0....2....0....0....0....2....0....2....2....1....1....1....2....1....1....2
%e ..0....0....0....0....0....1....1....0....0....1....2....0....0....0....1....2
%e ..1....0....0....0....0....0....0....0....0....0....0....2....1....0....0....0
%e ..1....0....1....2....0....0....2....1....0....2....0....0....1....0....0....1
%e ..0....0....2....1....1....0....1....0....1....1....0....0....1....1....1....0
%e ..1....1....1....2....2....1....0....1....2....0....0....1....0....2....0....0
%K nonn
%O 1,1
%A _R. H. Hardin_ May 25 2012
