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%I #22 May 26 2016 02:29:37
%S 2,8,18,33,54,82,118,163,218,284,362,453,558,678,814,967,1138,1328,
%T 1538,1769,2022,2298,2598,2923,3274,3652,4058,4493,4958,5454,5982,
%U 6543,7138,7768,8434,9137,9878,10658,11478,12339,13242
%N Number of n X 3 1..2 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 Empirical: a(n) = (n^3+6*n^2+11*n-6)/6.
%F a(n) = A167772(n+3,n). - _Philippe Deléham_, Nov 11 2009
%F a(n) = A227819(n+6,n+2). - _Alois P. Heinz_, Sep 22 2013
%F Empirical: a(n) = floor(A000292(n+1)^3/(A000292(n+1) + 1)^ 2). - _Ivan N. Ianakiev_, Nov 05 2013
%F From _G. C. Greubel_, May 25 2016: (Start)
%F Empirical G.f.: (-1 + 6*x - 6*x^2 + 2*x^3)/(1 - x)^4 + 1.
%F Empirical E.g.f.: (1/6)*(-6 + 18*x + 9*x^2 + x^3)*exp(x) + 1. (End)
%e All solutions for n=3
%e ...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1
%e ...1.1.1...1.1.1...1.1.1...2.1.1...2.1.1...2.1.1...2.2.1...2.2.1...2.2.2
%e ...2.1.1...2.2.1...2.2.2...2.1.1...2.2.1...2.2.2...2.2.1...2.2.2...2.2.2
%e ------
%e ...2.1.1...2.1.1...2.1.1...2.1.1...2.1.1...2.1.1...2.2.1...2.2.1...2.2.1
%e ...2.1.1...2.1.1...2.1.1...2.2.1...2.2.1...2.2.2...2.2.1...2.2.1...2.2.2
%e ...2.1.1...2.2.1...2.2.2...2.2.1...2.2.2...2.2.2...2.2.1...2.2.2...2.2.2
%t lst={};Do[AppendTo[lst,n*(n+1)*(n+2)/6-2],{n,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Feb 07 2010 *)
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 21 2009
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