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%I #10 May 27 2016 03:00:38
%S 6,90,454,1541,4186,9808,20646,40039,72750,125334,206550,327817,
%T 503714,752524,1096822,1564107,2187478,3006354,4067238,5424525,
%U 7141354,9290504
%N Number of n X 3 1..3 arrays containing at least one of each value, all equal values connected, and rows considered as a single number in nondecreasing order.
%F Empirical: a(n) = (11*n^6 + 57*n^5 + 545*n^4 + 285*n^3 + 1424*n^2 - 1782*n + 540)/180.
%F From _G. C. Greubel_, May 26 2016: (Start)
%F Empirical G.f.: x*(3*x^6 + x^5 - 7*x^4 + 43*x^3 - 50*x^2 + 48*x + 6 ) ) / (1-x)^7.
%F Empirical E.g.f.: (1/180)*(540 + 540*x + 7290*x^2 + 5970*x^3 + 1830*x^4 + 222*x^5 + 11*x^6)*exp(x) - 3. (End)
%e Some solutions for n=4:
%e ...2.1.1...1.1.1...2.1.1...3.1.1...2.1.1...3.2.1...1.2.2...2.2.2...1.1.1
%e ...2.2.2...1.1.1...3.3.1...3.1.1...2.2.2...3.2.1...3.2.3...3.2.1...1.1.1
%e ...3.2.2...1.1.3...3.3.3...3.1.1...2.2.2...3.2.1...3.3.3...3.3.1...2.3.1
%e ...3.3.2...1.2.2...3.3.3...3.2.1...3.3.2...3.3.3...3.3.3...3.3.1...3.3.3
%e ------
%e ...1.1.1...2.2.1...1.2.2...1.3.2...3.1.1...1.1.1...3.1.1...1.2.3...1.1.2
%e ...3.2.1...2.2.2...2.2.2...1.3.2...3.2.2...1.1.3...3.1.1...1.2.3...1.1.3
%e ...3.3.1...3.3.2...2.3.3...1.3.3...3.3.2...2.2.3...3.2.1...1.2.3...3.3.3
%e ...3.3.1...3.3.3...3.3.3...1.3.3...3.3.3...2.2.3...3.2.2...1.3.3...3.3.3
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 21 2009
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