A166839 - OEIS

%I #12 May 26 2016 02:30:14

%S 0,0,55,478,2166,7120,19219,45316,96732,191232,355575,628738,1065922,

%T 1743456,2764723,4267240,6431032,9488448,13735575,19545414,27382990,

%U 37822576,51567219,69470764,92562580,122075200

%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 decreasing order.

%F Empirical: a(n) = (1/7!)*n*(n-1)*(n-2)*(n^5 + 35*n^4 + 523*n^3 + 3361*n^2 + 4396*n - 14436).

%F From _G. C. Greubel_, May 25 2016: (Start)

%F Empirical G.f.: x^3*(55 - 17*x - 156*x^2 + 214*x^3 - 107*x^4 + 19*x^5)/(1 - x)^9.

%F Empirical E.g.f.: (1/7!)*x^3*(46200 + 54180*x + 13692*x^2 + 1358*x^3 + 60*x^4 + x^5)*exp(x). (End)

%e Some solutions for n=4

%e ...3.2...3.2...3.2...2.1...2.1...3.1...2.1...3.1...2.1...2.1...2.2...1.1...2.2

%e ...4.2...3.5...5.1...3.1...2.1...3.2...4.1...3.2...2.3...2.2...4.1...2.1...3.2

%e ...5.1...4.1...5.4...4.5...3.4...3.4...5.3...3.3...5.4...3.4...5.3...2.4...4.2

%e ...5.5...4.4...5.4...4.5...5.4...5.4...5.3...5.4...5.5...5.4...5.3...5.3...5.1

%e ------

%e ...2.2...1.1...3.1...2.1...4.3...4.2...1.1...2.2...3.2...3.2...4.1...1.1...2.1

%e ...3.1...2.1...3.1...3.3...5.1...4.3...3.1...2.2...4.2...3.2...4.1...3.1...2.2

%e ...4.1...3.4...3.5...3.4...5.2...4.4...4.4...3.1...4.2...3.4...4.3...4.2...2.4

%e ...4.5...5.4...4.2...3.5...5.5...5.1...5.2...4.5...5.1...5.1...5.2...4.5...5.3

%K nonn

%O 1,3

%A _R. H. Hardin_, Oct 21 2009