%I #10 May 26 2016 02:29:59

%S 0,4,49,218,662,1626,3479,6748,12156,20664,33517,52294,78962,115934,

%T 166131,233048,320824,434316,579177,761938,990094,1272194,1617935,

%U 2038260,2545460,3153280,3877029,4733694,5742058,6922822,8298731,9894704

%N Number of nX2 1..4 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 decreasing order.

%H R. H. Hardin, <a href="/A166838/b166838.txt">Table of n, a(n) for n=1..44</a>

%F Empirical: a(n) = (n^6 + 18*n^5 + 100*n^4 - 30*n^3 - 551*n^2 + 462*n)/180.

%F From _G. C. Greubel_, May 25 2016: (Start)

%F Empirical G.f.: x^2*(4 + 21*x - 41*x^2 + 25*x^3 - 5*x^4)/(1 - x)^7.

%F Empirical E.g.f.: (1/180)*x^2*(360 + 1110*x + 345*x^2 + 33*x^3 + x^4)*exp(x). (End)

%e All solutions for n=3

%e ...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.1...2.1...2.1...2.1...2.1

%e ...2.1...2.1...2.2...3.1...3.2...3.2...3.2...3.3...4.2...2.1...2.1...2.2...2.2

%e ...3.4...4.3...4.3...4.2...3.4...4.2...4.4...4.2...4.3...3.4...4.3...3.4...4.3

%e ------

%e ...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1

%e ...2.3...2.3...2.3...2.4...2.4...3.1...3.1...3.1...3.3...3.3...3.3...3.4...3.4

%e ...2.4...4.3...4.4...3.3...3.4...3.4...4.1...4.4...3.4...4.3...4.4...3.4...4.4

%e ------

%e ...2.1...2.1...2.1...2.2...2.2...2.2...2.2...2.2...2.2...3.1...3.1...3.1...3.1

%e ...4.1...4.3...4.3...3.1...3.1...3.1...3.2...3.3...4.1...3.1...3.2...3.2...3.2

%e ...4.3...4.3...4.4...3.4...4.1...4.4...4.1...4.1...4.3...4.2...3.4...4.2...4.4

%e ------

%e ...3.1...3.1...3.1...3.1...3.2...3.2...3.2...3.2...3.3...4.1

%e ...3.3...4.1...4.2...4.2...3.2...3.3...4.1...4.1...4.1...4.2

%e ...4.2...4.2...4.2...4.4...4.1...4.1...4.1...4.4...4.2...4.3

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 21 2009