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%I #3 Mar 31 2012 12:35:35
%S 101,233,265,335,409,483,557,631,705,779,853,927,1001,1075,1149,1223
%N Number of slanted nX6 (i=1..n)X(j=i..6+i-1) 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>=7
%e Some solutions for n=3
%e ...1.1.1.1.2.2.......1.1.2.2.2.2.......1.1.1.1.1.2.......1.1.1.2.2.2....
%e .....3.3.1.2.4.4.......3.3.4.4.2.2.......3.3.4.1.2.2.......3.3.2.4.2.2..
%e .......3.3.3.3.4.4.......3.3.4.4.4.4.......3.4.4.4.4.4.......3.2.4.4.4.4
%e ------
%e ...1.1.2.2.2.2.......1.1.1.2.2.2.......1.1.4.4.4.2.......1.2.2.2.2.2....
%e .....1.1.1.4.2.2.......2.2.2.4.4.4.......1.1.1.4.4.4.......2.4.4.4.4.4..
%e .......3.3.4.4.4.4.......3.3.3.3.4.4.......3.3.3.3.4.4.......3.3.3.3.4.4
%K nonn
%O 2,1
%A _R. H. Hardin_ Sep 17 2009
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