%I #14 Jun 22 2022 12:05:38
%S 0,0,30,728,5364,24402,84285,242793,614140,1407960,2987500,5953706,
%T 11263472,20392138,35552387,59984019,98331688,157130592,245423322
%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 nonincreasing order.
%F From _G. C. Greubel_, May 25 2016: (Start)
%F Empirical: a(n) = (16/(10)!)*(n-1)*(n-2)*(n^8 + 53*n^7 + 1342*n^6 + 17630*n^5 + 91114*n^4 - 102013*n^3 - 1246977*n^2 + 1575810*n - 113400).
%F Empirical G.f.: (1 - 11*x + 55*x^2 - 195*x^3 - 68*x^4 + 532*x^5 - 26*x^6 - 993*x^7 + 1077*x^8 - 461*x^9 + 73*x^10)/(x -1)^11 + 1.
%F Empirical E.g.f.: (16/(10)!)*(-226800 + 226800*x - 113400*x^2 + 1171800*x^3 + 5736150*x^4 + 3827250*x^5 + 799155*x^6 + 75870*x^7 + 3735*x^8 + 95*x^9 + x^10)*exp(x) + 1. (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,more
%O 1,3
%A _R. H. Hardin_, Oct 21 2009