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A212730 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) 1

%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*n-1)*(16*n^2 - 60*n + 53)*a(n) = (608*n^4 - 3032*n^3 + 5050*n^2 - 3259*n + 660)*a(n-1) - 9*(352*n^4 - 2008*n^3 + 3986*n^2 - 3143*n + 750)*a(n-2) + 81*(n-2)*(2*n-5)*(16*n^2 - 28*n + 9)*a(n-3).

%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

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Last modified February 1 03:56 EST 2023. Contains 359981 sequences. (Running on oeis4.)