A166814 - OEIS

%I #6 Nov 23 2015 15:50:14

%S 0,6,25,66,140,260,441,700,1056,1530,2145,2926,3900,5096,6545,8280,

%T 10336,12750,15561,18810,22540,26796,31625,37076,43200,50050,57681,

%U 66150,75516,85840,97185,109616,123200,138006,154105,171570,190476,210900,232921

%N Number of nX2 1..3 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.

%H R. H. Hardin, <a href="/A166814/b166814.txt">Table of n, a(n) for n=1..83</a>

%F Empirical: a(n)=(n^4+8*n^3+5*n^2-14*n)/12.

%F Empirical: G.f.: -x^2*(x-2)*(x-3) / (x-1)^5 . - _R. J. Mathar_, Nov 23 2015

%e All solutions for n=3

%e ...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.2...1.1...1.1

%e ...2.2...2.2...2.2...1.2...1.2...1.2...1.3...1.3...3.2...3.2...3.3...2.2...2.3

%e ...2.3...3.2...3.3...1.3...3.2...3.3...1.3...3.3...3.2...3.3...3.3...2.3...2.3

%e ------

%e ...1.1...1.1...1.1...1.1...1.1...1.1...1.1...1.3...1.3...1.3...1.3...1.3

%e ...2.3...1.2...1.2...1.2...1.1...1.3...1.3...2.2...2.3...2.3...1.3...1.3

%e ...3.3...1.3...3.2...3.3...2.3...2.2...2.3...2.2...2.3...3.3...2.2...2.3

%K nonn

%O 1,2

%A _R. H. Hardin_ Oct 21 2009