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%I #9 Aug 20 2018 05:50:28
%S 2,9,57,366,2358,15204,98052,632376,4078488,26304144,169648272,
%T 1094144736,7056675168,45511953984,293528880192,1893111501696,
%U 12209603211648,78745710676224,507869653293312,3275500119584256
%N Number of n X 2 0..2 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..2 introduced in row major order.
%C Column 2 of A223387.
%H R. H. Hardin, <a href="/A223381/b223381.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 8*a(n-1) - 10*a(n-2) for n>3.
%F Conjectures from _Colin Barker_, Aug 20 2018: (Start)
%F G.f.: x*(1 - x)*(2 - 5*x) / (1 - 8*x + 10*x^2).
%F a(n) = (-(4-sqrt(6))^n*(-6+sqrt(6)) + (4+sqrt(6))^n*(6+sqrt(6))) / 40 for n>1.
%F (End)
%e Some solutions for n=3:
%e ..0..1....0..1....0..0....0..0....0..1....0..1....0..1....0..1....0..1....0..1
%e ..2..0....2..1....1..2....1..1....0..2....0..2....2..0....2..0....0..2....0..1
%e ..0..2....0..2....0..2....0..2....2..0....0..1....1..1....2..1....1..0....0..1
%Y Cf. A223387.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 19 2013