A166832 - OEIS

%I #11 May 26 2016 02:25:58

%S 0,49,574,3170,12373,39110,106825,261632,588256,1233991,2443430,

%T 4607306

%N Number of nX3 1..4 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 nonincreasing order.

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

%F Empirical: a(n) = (1/181440)*n*(n-1)*(-1105344 + 219960*n + 516656*n^2 + 235676*n^3 + 53879*n^4 + 8015*n^5 + 569*n^6 + 29*n^7).

%F Empirical G.f.: x^2*(49 + 84*x - 365*x^2 + 623*x^3 - 560*x^4 + 302*x^5 - 86*x^6 + 11*x^7)/(1 - x)^10.

%F Empirical E.g.f.: (1/181440)*x^2*(4445280 + 12912480*x + 8830080*x^2 + 2680776*x^3 + 422604*x^4 + 35964*x^5 + 1584*x^6 + 29*x^7)*exp(x). (End)

%e Some solutions for n=4

%e ...1.1.1...2.1.1...1.1.1...2.1.1...2.2.1...2.2.1...3.2.1...4.2.1...2.1.1

%e ...2.2.2...2.2.1...2.1.1...2.4.4...3.1.1...4.2.2...3.2.1...4.3.1...2.1.1

%e ...3.3.3...2.3.3...2.3.3...2.4.4...3.1.4...4.3.2...3.3.1...4.3.3...2.3.1

%e ...4.3.3...2.3.4...4.4.4...3.3.3...3.3.4...4.4.2...4.3.3...4.4.4...2.4.4

%e ------

%e ...2.2.1...1.1.1...3.3.2...1.1.1...3.2.1...2.2.1...3.1.1...3.3.1...2.2.1

%e ...2.2.1...4.1.1...4.3.3...3.1.1...3.3.3...3.2.2...3.2.1...4.3.3...4.2.1

%e ...3.3.3...4.3.2...4.3.3...3.3.2...3.3.4...3.4.2...3.2.4...4.4.2...4.3.3

%e ...3.3.4...4.3.2...4.4.1...4.4.4...4.4.4...4.4.4...4.4.4...4.4.4...4.3.3

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 21 2009