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%I #9 May 27 2016 03:01:13
%S 0,12,51,135,286,530,897,1421,2140,3096,4335,5907,7866,10270,13181,
%T 16665,20792,25636,31275,37791,45270,53802,63481,74405,86676,100400,
%U 115687,132651,151410,172086,194805,219697,246896,276540,308771,343735,381582
%N Number of nX2 1..3 arrays containing at least one of each value, all equal values connected, and rows considered as a single number in nondecreasing order.
%H R. H. Hardin, <a href="/A166776/b166776.txt">Table of n, a(n) for n=1..83</a>
%F Empirical: a(n) = (n^4 + 8*n^3 + 8*n^2 - 23*n + 6)/6.
%F From _G. C. Greubel_, May 26 2016: (Start)
%F Empirical G.f.: x^2*(x^3 - 9*x + 12)/(1-x)^5.
%F Empirical E.g.f.: (1/6)*(6 - 6*x + 39*x^2 + 14*x^3 + x^4)*exp(x) - 1. (End)
%e All solutions for n=3
%e ...2.2...2.2...2.2...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1
%e ...2.2...3.1...3.1...2.2...2.2...2.2...2.1...2.1...2.1...2.3...2.3...3.1...3.1
%e ...3.1...3.1...3.3...2.3...3.2...3.3...2.3...3.1...3.3...2.3...3.3...3.1...3.3
%e ------
%e ...2.1...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.1
%e ...3.3...2.2...2.2...2.2...1.2...1.2...1.2...1.3...1.3...3.2...3.2...3.3...2.2
%e ...3.3...2.3...3.2...3.3...1.3...3.2...3.3...1.3...3.3...3.2...3.3...3.3...2.3
%e ------
%e ...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1
%e ...2.2...2.2...2.1...2.1...2.1...2.3...2.3...1.2...1.2...1.2...1.1...1.1...1.3
%e ...3.2...3.3...2.3...3.1...3.3...2.3...3.3...1.3...3.2...3.3...2.3...3.2...2.2
%e ------
%e ...1.1...1.1...1.1...1.1...1.3...1.3...1.3...1.3...1.3...3.1...3.1...3.1
%e ...1.3...3.2...3.2...3.1...2.2...2.3...2.3...1.3...1.3...3.2...3.2...3.1
%e ...2.3...3.2...3.3...3.2...2.2...2.3...3.3...2.2...2.3...3.2...3.3...3.2
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 21 2009
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