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%I #7 Oct 26 2018 08:58:58
%S 1,1,6,13,47,128,405,1181,3598,10705,32259,96544,290009,869417,
%T 2609238,7826117,23480935,70438624,211322637,633956965,1901888606,
%U 5705637161,17116957851,51350798528,154052516977,462157354513,1386472381350
%N Number of (n+1) X (1+1) 0..2 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..2 introduced in row major order.
%H R. H. Hardin, <a href="/A239530/b239530.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) + 4*a(n-2) - 3*a(n-3).
%F Conjectures from _Colin Barker_, Oct 26 2018: (Start)
%F G.f.: x*(1 - x) / ((1 - 3*x)*(1 + x - x^2)).
%F a(n) = (10*3^n + 2^(-n)*((-1+sqrt(5))^n*(-5+4*sqrt(5)) - (-1-sqrt(5))^n*(5+4*sqrt(5)))) / 55.
%F (End)
%e Some solutions for n=5:
%e ..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
%e ..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
%e ..0..2....2..0....1..0....1..0....1..0....0..2....2..0....2..1....2..1....1..0
%e ..0..2....2..0....1..0....1..0....1..0....0..2....2..0....2..1....2..0....1..0
%e ..1..2....1..0....0..1....1..0....2..1....2..0....0..2....0..2....1..0....0..2
%e ..1..2....1..0....0..1....1..0....2..1....2..0....0..2....0..2....1..0....0..2
%Y Column 1 of A239537.
%K nonn
%O 1,3
%A _R. H. Hardin_, Mar 21 2014
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