A166776 - OEIS

%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