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%I #12 Jul 31 2013 09:23:43
%S 8,148,1669,16878,163495,1549297,14492156,134429604,1239807015,
%T 11386939467,104257566078,952281922551,8681609266794,79026329849968,
%U 718456060049941,6524950672498742,59207190970359999,536844632687526915
%N Number of 0..2 arrays of length 2*n+2 with sum less than 2*n in any length 2n subsequence (=less than 50% duty cycle)
%C Row 3 of A212729
%H R. H. Hardin, <a href="/A212732/b212732.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)*(59040*n^4 - 630664*n^3 + 2419338*n^2 - 3925427*n + 2259783)*a(n) = (2243520*n^6 - 26740112*n^5 + 122386084*n^4 - 271040464*n^3 + 300314759*n^2 - 153351297*n + 26751060)*a(n-1) + 81*(n-3)*(2*n-7)*(59040*n^4 - 394504*n^3 + 881586*n^2 - 742583*n + 182070)*a(n-3) - 9*(1298880*n^6 - 16413328*n^5 + 81293588*n^4 - 199839104*n^3 + 252840847*n^2 - 150974403*n + 30574530)*a(n-2)
%F Conjecture: a(n) ~ 9/2*9^n. (End)
%e Some solutions for n=3
%e ..2....0....1....1....2....0....0....0....0....1....0....1....1....0....1....0
%e ..0....0....0....0....0....1....0....0....1....1....2....0....0....1....0....2
%e ..0....1....1....0....0....0....1....2....1....0....0....1....0....1....0....1
%e ..2....2....1....2....1....1....0....1....0....1....1....0....0....0....0....0
%e ..0....1....0....0....1....0....1....0....0....1....0....1....2....0....0....0
%e ..0....0....0....0....0....2....0....0....0....0....1....1....0....1....0....0
%e ..0....1....1....1....2....0....0....0....1....0....0....0....0....2....0....2
%e ..2....0....1....0....0....2....2....1....1....2....0....2....1....0....0....1
%K nonn
%O 1,1
%A _R. H. Hardin_ May 25 2012
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