A166796 - OEIS

%I #8 May 27 2016 03:00:34

%S 0,6,26,69,146,270,456,721,1084,1566,2190,2981,3966,5174,6636,8385,

%T 10456,12886,15714,18981,22730,27006,31856,37329,43476,50350,58006,

%U 66501,75894,86246,97620,110081,123696,138534,154666,172165,191106,211566,233624

%N Number of nX2 1..3 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nondecreasing order.

%H R. H. Hardin, <a href="/A166796/b166796.txt">Table of n, a(n) for n=1..83</a>

%F Empirical: a(n) = (n^4 + 8*n^3 + 11*n^2 - 32*n + 12)/12.

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

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

%F Empirical E.g.f.: (1/12)*(12 - 12*x + 42*x^2 + 14*x^3 + x^4)*exp(x) - 1. (End)

%e All solutions for n=3

%e ...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.1...1.1

%e ...2.2...2.2...2.2...1.2...1.2...1.2...1.3...1.3...3.2...3.2...3.3...2.2...2.2

%e ...2.3...3.2...3.3...1.3...3.2...3.3...1.3...3.3...3.2...3.3...3.3...2.3...3.3

%e ------

%e ...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.3...1.3...1.3...1.3...1.3

%e ...2.3...2.3...1.2...1.2...1.2...1.1...1.3...1.3...2.2...2.3...2.3...1.3...1.3

%e ...2.3...3.3...1.3...3.2...3.3...2.3...2.2...2.3...2.2...2.3...3.3...2.2...2.3

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 21 2009