A166757 - OEIS

%I #13 May 27 2016 03:00:43

%S 0,24,504,3672,16272,53784,146184,345240,733344,1433880,2623128,

%T 4543704,7519536,11972376,18439848,27595032,40267584,57466392,

%U 80403768,110521176,149516496,199372824,262388808,341210520,438864864,558794520,704894424

%N Number of nX2 1..4 arrays containing at least one of each value, and all equal values connected.

%H R. H. Hardin, <a href="/A166757/b166757.txt">Table of n, a(n) for n=1..45</a>

%F Empirical: a(n) = (4/15)*(n-1)*(8*n^5 -28*n^4 + 97*n^3 - 218*n^2 + 234*n -90).

%F From _G. C. Greubel_, May 26 2016: (Start)

%F Empirical G.f.: 24*x^2*(x^5 + 8*x^4 + 13*x^3 + 27*x^2 + 14*x + 1)/(1-x)^7.

%F Empirical E.g.f.: (4/15)*(90 - 90*x + 90*x^2 + 255*x^3 + 285*x^4 + 84*x^5 + 8*x^6)*exp(x) - 24. (End)

%e Some solutions for n=4

%e ...2.1...3.1...3.4...2.4...4.1...1.4...2.2...3.1...1.4...3.1...3.1...2.2...1.4

%e ...3.3...1.1...3.4...2.2...1.1...2.2...4.1...1.1...2.4...3.1...3.2...2.1...1.3

%e ...3.4...1.2...3.4...1.1...3.1...3.2...3.1...2.1...2.3...3.3...2.2...2.2...1.2

%e ...4.4...4.4...1.2...3.1...3.2...3.2...3.1...2.4...2.3...2.4...4.2...4.3...1.1

%e ------

%e ...4.3...2.3...4.4...4.4...3.3...3.3...2.4...3.3...1.3...1.3...3.3...4.4...1.2

%e ...1.3...2.2...1.1...3.4...3.1...4.4...1.1...2.1...2.3...4.4...3.4...3.4...4.4

%e ...2.3...4.4...3.2...3.1...4.1...4.1...1.1...2.4...2.3...4.4...1.1...3.4...4.4

%e ...3.3...1.1...3.2...2.2...2.1...2.2...1.3...4.4...4.4...2.4...2.1...2.1...4.3

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 21 2009