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%I #11 May 26 2016 02:27:46
%S 0,0,30,728,5364,24401,84279,242772,614084,1407834,2987248,5953244,
%T 11262680,20390851,35550385,59981016,98327320,157124404,245414754
%N Number of n X 2 1..6 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.
%F From _G. C. Greubel_, May 25 2016: (Start)
%F Empirical a(n) = (16/(10)!)*n*(n-1)*(n-2)*(1486980 - 1224297*n - 103903*n^2 + 91114*n^3 + 17630*n^4 + 1342*n^5 + 53*n^6 + n^7).
%F Empirical G.f.: x^3*(30 + 398*x - 994*x^2 + 487*x^3 + 668*x^4 - 922*x^5 + 416*x^6 - 67*x^7)/(1 - x)^11.
%F Empirical E.g.f.: (16/(10)!)*x^3*(1134000 + 5745600*x + 3825360*x^2 + 799155*x^3 + 75870*x^4 + 3735*x^5 + 95*x^6 + x^7)*exp(x). (End)
%e All solutions for n=3
%e ...4.3...4.3...3.1...3.1...3.1...3.1...3.2...3.2...3.2...3.2...3.1...3.1...3.2
%e ...5.1...5.2...4.2...4.2...4.5...4.6...4.1...4.1...4.5...4.6...5.4...5.2...5.4
%e ...6.2...6.1...5.6...6.5...6.2...5.2...5.6...6.5...6.1...5.1...6.2...6.4...6.1
%e ------
%e ...3.2...4.1...4.1...4.2...4.2...2.1...2.1...2.1...2.1...2.1...2.1...2.1...2.1
%e ...5.1...5.3...5.2...5.3...5.1...3.4...3.4...3.5...3.5...3.6...3.6...4.3...4.3
%e ...6.4...6.2...6.3...6.1...6.3...5.6...6.5...6.4...4.6...5.4...4.5...5.6...6.5
%e ------
%e ...2.1...2.1...2.1...2.1
%e ...4.5...4.6...5.3...5.4
%e ...6.3...5.3...6.4...6.3
%K nonn
%O 1,3
%A _R. H. Hardin_, Oct 21 2009
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