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%I #10 May 26 2016 11:27:31
%S 0,0,720,32400,434160,3309120,17807040,75294000,266274720,819872640,
%T 2259483120,5685633360,13259846160,28992150720,59970549600,
%U 118213974000,223381776960
%N Number of nX2 1..6 arrays containing at least one of each value, and all equal values connected.
%F From _G. C. Greubel_, May 26 2016: (Start)
%F Empirical a(n) = (2/315)*(n-1)*(n-2)*(32*n^8 - 304*n^7 + 2744*n^6 - 15880*n^5 + 62078*n^4 - 171871*n^3 + 319311*n^2 - 353880*n + 170100).
%F Empirical G.f.: 720*x^3*(3*x+1)*(x^7 + 8*x^6 + 25*x^5 + 57*x^4 + 63*x^3 + 70*x^2 + 31*x + 1)/(1-x)^11.
%F Empirical E.g.f.: (2/315)*(340200 - 340200*x + 170100*x^2 - 37800*x^3 + 207900*x^4 + 363825*x^5 + 257670*x^6 + 82800*x^7 + 13320*x^8 + 1040*x^9 + 32*x^10)*exp(x) - 2160. (End)
%e Some solutions for n=3
%e ...4.1...1.4...2.5...5.2...6.4...4.6...3.6...3.2...3.5...2.6...2.5...1.2...4.1
%e ...6.5...5.2...4.3...3.6...5.3...1.2...4.1...6.5...6.2...4.1...3.1...5.3...6.3
%e ...3.2...6.3...1.6...1.4...2.1...5.3...2.5...1.4...1.4...3.5...6.4...4.6...5.2
%e ------
%e ...3.2...5.3...1.5...5.4...1.6...2.6...1.6...1.3...4.1...6.4...6.4...3.4...3.6
%e ...4.5...4.1...3.6...1.6...4.5...3.4...5.2...2.6...5.6...3.2...1.3...6.2...4.1
%e ...1.6...2.6...2.4...3.2...2.3...5.1...4.3...4.5...2.3...1.5...2.5...1.5...5.2
%K nonn
%O 1,3
%A _R. H. Hardin_, Oct 21 2009
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