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%I #3 Mar 31 2012 12:35:35
%S 8,80,258,480,644,752,850,956,1070,1184,1298,1412,1526,1640,1754,1868,
%T 1982,2096,2210,2324,2438,2552,2666,2780,2894,3008,3122,3236,3350,
%U 3464,3578,3692,3806,3920,4034,4148,4262
%N Number of nX3 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, 4 in the lower right corner, and with no element having more than 2 neighbors with the same value
%F Empirical: a(n)=2*a(n-1)-a(n-2) for n>=11
%e Some solutions for n=4
%e ...1.1.2...1.1.2...1.2.2...1.2.2...1.1.2...1.2.2...1.2.2...1.2.2...1.4.2
%e ...1.1.2...3.2.2...1.2.4...1.3.4...1.2.2...2.2.3...1.2.2...1.1.4...1.4.2
%e ...3.4.2...3.2.4...2.2.4...1.3.4...3.3.4...3.3.3...1.4.4...3.1.4...1.4.2
%e ...3.4.4...3.4.4...3.4.4...3.3.4...3.3.4...3.4.4...3.3.4...3.4.4...3.4.4
%e ------
%e ...1.2.2...1.1.2...1.2.2...1.2.2...1.1.2...1.1.2...1.1.2...1.2.2...1.1.2
%e ...3.3.2...3.1.2...1.1.2...1.1.2...1.4.2...1.2.2...3.1.2...1.1.2...2.2.2
%e ...3.4.2...3.2.2...3.1.2...3.1.2...1.4.2...1.2.4...3.2.2...3.1.4...2.4.4
%e ...3.4.4...3.3.4...3.3.4...3.1.4...3.4.4...3.4.4...3.4.4...3.1.4...3.3.4
%K nonn
%O 2,1
%A _R. H. Hardin_ Aug 24 2009
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