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A166756 Number of nX2 1..3 arrays containing at least one of each value, and all equal values connected. 1

%I

%S 0,24,174,642,1716,3780,7314,12894,21192,32976,49110,70554,98364,

%T 133692,177786,231990,297744,376584,470142,580146,708420,856884,

%U 1027554,1222542,1444056,1694400,1975974,2291274,2642892,3033516,3465930,3943014,4467744

%N Number of nX2 1..3 arrays containing at least one of each value, and all equal values connected.

%H R. H. Hardin, <a href="/A166756/b166756.txt">Table of n, a(n) for n=1..82</a>

%F Empirical: a(n) = 4*n^4 - 8*n^3 + 11*n^2 - 13*n + 6.

%F From _G. C. Greubel_, May 26 2016: (Start)

%F Empirical G.f.: 6*x^2*(x^3 + 2*x^2 + 9*x + 4)/(1 - x)^5.

%F Empirical E.g.f.: (6 - 6*x + 15*x^2 + 16*x^3 + 4*x^4)*exp(x) - 6. (End)

%e Some solutions for n=4

%e ...1.1...2.3...1.1...3.2...3.3...2.2...2.2...3.1...2.3...2.3...2.1...3.3...1.1

%e ...1.3...2.1...3.1...2.2...3.1...1.2...2.1...2.1...2.2...2.3...2.1...3.2...2.1

%e ...1.2...2.2...2.1...1.1...3.1...1.1...2.3...1.1...2.1...2.3...1.1...3.1...3.3

%e ...2.2...2.2...1.1...1.1...2.1...3.3...3.3...1.1...1.1...1.1...3.3...1.1...3.3

%e ------

%e ...3.3...1.3...1.2...1.2...3.3...3.1...3.2...3.3...2.1...3.2...1.1...2.2...1.1

%e ...3.1...1.1...1.2...1.3...3.3...3.3...3.3...3.2...1.1...3.3...1.3...2.1...2.2

%e ...1.1...1.2...1.1...3.3...1.1...3.3...3.3...2.2...3.1...3.3...1.1...2.2...2.2

%e ...2.1...2.2...3.1...3.3...2.1...2.2...1.1...2.1...1.1...1.3...2.2...3.2...2.3

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 21 2009

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Last modified December 1 05:02 EST 2022. Contains 358454 sequences. (Running on oeis4.)