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%I #4 Apr 15 2014 18:22:04
%S 2,12,67,386,2333,14438,90729,576616,3692697,23768052,153496623,
%T 993485284,6439467991,41777922610,271212402395,1761347749066,
%U 11441763716997,74338495106470,483038660675361,3138923546597920
%N Number of nX3 0..2 arrays with no element equal to exactly one horizontal or vertical neighbor, with new values 0..2 introduced in row major order
%C Column 3 of A241078
%H R. H. Hardin, <a href="/A241074/b241074.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 13*a(n-1) -53*a(n-2) +90*a(n-3) -196*a(n-4) +404*a(n-5) +124*a(n-6) +242*a(n-7) -955*a(n-8) -3141*a(n-9) -2695*a(n-10) +1876*a(n-11) +9112*a(n-12) +7732*a(n-13) +8168*a(n-14) -12592*a(n-15) -17664*a(n-16) -3904*a(n-17) +11648*a(n-18) +4864*a(n-19) -3072*a(n-20) for n>21
%e Some solutions for n=4
%e ..0..1..2....0..1..2....0..1..2....0..0..1....0..1..0....0..1..0....0..0..0
%e ..2..0..1....1..0..1....1..2..0....0..0..0....2..0..2....1..2..1....0..1..0
%e ..1..1..2....0..1..0....0..1..2....1..0..0....0..1..0....0..0..0....0..0..0
%e ..1..1..0....1..0..2....1..0..1....2..1..2....1..0..2....0..0..0....2..0..0
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 15 2014