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%I #12 May 26 2016 07:46:47
%S 0,0,90,1552,9902,41151,133175,364772,885824,1962990,4046548,7865396,
%T 14558830,25855557,44312489,73628216,119048688,187885564,290170926
%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 increasing order.
%F Empirical: a(n) = (16/10!)*n*(n-1)*(n-2)*(361620 - 1844397*n + 175952*n^2 + 173779*n^3 + 23435*n^4 + 1477*n^5 + 53*n^6 + n^7). - _G. C. Greubel_, May 25 2016
%F Empirical g.f.: x^3*(90+562*x-2220*x^2+2739*x^3-1256*x^4-98*x^5+258*x^6-59*x^7) / (1-x)^11. - _Colin Barker_, May 25 2016
%e Some solutions for n=4
%e ...1.5...1.4...2.3...1.1...2.6...1.1...1.2...1.3...1.3...2.4...1.1...1.4...3.6
%e ...4.2...2.6...5.1...2.4...4.3...1.3...3.3...5.2...2.4...5.3...1.5...5.2...4.1
%e ...4.2...3.3...5.4...3.5...4.3...2.5...4.6...5.4...2.6...5.5...3.4...5.3...4.2
%e ...6.3...5.5...5.6...6.6...5.1...4.6...5.6...6.4...5.6...6.1...6.2...5.6...5.2
%e ------
%e ...1.2...2.5...1.6...1.6...1.5...1.2...2.4...2.4...1.1...1.4...1.4...2.3...1.4
%e ...2.2...4.1...2.2...4.3...3.2...1.5...2.4...2.4...1.4...2.5...2.2...2.3...2.2
%e ...3.5...6.3...3.4...5.2...3.2...6.3...3.6...3.1...3.5...3.5...2.5...4.1...2.5
%e ...6.4...6.6...5.5...5.2...6.4...6.4...5.1...6.5...6.2...6.6...6.3...5.6...3.6
%K nonn
%O 1,3
%A _R. H. Hardin_, Oct 21 2009