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%I #7 May 27 2016 03:00:28
%S 0,0,105,767,3160,9756,25163,57293,118936,229824,419277,729531,
%T 1219856,1971580,3094143,4732313,7074704,10363744,14907249,21091767,
%U 29397864,40417532,54873907,73643493,97781096,128547680
%N Number of nX2 1..5 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.
%F Empirical: a(n) = (n^8 + 32*n^7 + 476*n^6 + 3038*n^5 - 1141*n^4 - 35182*n^3 + 53584*n^2 - 25848*n + 5040)/5040.
%F From _G. C. Greubel_, May 26 2016: (Start)
%F Empirical G.f.: x^3*(x^6 + 14*x^5 - 79*x^4 + 108*x^3 + 37*x^2 - 178*x + 105 ) /(1-x)^9.
%F Empirical E.g.f.: (1/5040)*(5040 - 5040*x + 2520*x^2 + 87360*x^3 + 73080*x^4 + 15708*x^5 + 1414*x^6 + 60*x^7 + x^8)*exp(x) - 1. (End)
%e Some solutions for n=4
%e ...1.3...2.3...1.2...1.4...1.2...1.4...1.3...1.4...2.4...1.2...1.2...1.1...1.5
%e ...4.2...4.3...4.2...1.4...3.3...2.2...2.3...3.2...3.1...3.4...2.2...1.4...2.2
%e ...4.5...5.1...4.3...2.3...3.3...2.3...4.4...3.2...3.3...4.4...2.3...2.2...3.4
%e ...5.5...5.1...4.5...2.5...4.5...2.5...4.5...3.5...3.5...4.5...5.4...3.5...4.4
%e ------
%e ...2.3...1.4...1.2...1.4...1.5...1.1...1.1...1.3...1.2...1.2...1.2...1.2...1.1
%e ...3.3...3.2...1.4...3.4...2.2...2.3...1.2...3.3...3.3...3.2...5.3...4.3...2.3
%e ...4.1...3.3...3.3...3.4...3.3...4.5...4.3...4.4...3.4...4.2...5.4...5.3...3.3
%e ...4.5...5.3...3.5...5.2...4.3...4.5...4.5...5.2...5.4...5.5...5.4...5.3...5.4
%K nonn
%O 1,3
%A _R. H. Hardin_, Oct 21 2009
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