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A184368 1/3 the number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having at least two equal elements connected horizontally or vertically.

%I A184368 #8 Feb 27 2018 08:44:08
%S A184368 21,153,1107,8019,58077,420633,3046491,22064643,159806277,1157419449,
%T A184368 8382773187,60713414163,439725443661,3184773389433,23066169329547,
%U A184368 167059976482179,1209955382858997,8763272085493593,63469230958692531
%N A184368 1/3 the number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having at least two equal elements connected horizontally or vertically.
%C A184368 Column 1 of A184376.
%H A184368 R. H. Hardin, <a href="/A184368/b184368.txt">Table of n, a(n) for n = 1..200</a>
%F A184368 Empirical: a(n) = 6*a(n-1) + 9*a(n-2).
%F A184368 Conjectures from _Colin Barker_, Feb 27 2018: (Start)
%F A184368 G.f.: 3*x*(7 + 9*x) / (1 - 6*x - 9*x^2).
%F A184368 a(n) = ((3-3*sqrt(2))^n*(-4+3*sqrt(2)) + (3*(1+sqrt(2)))^n*(4+3*sqrt(2))) / (2*sqrt(2)).
%F A184368 (End)
%e A184368 Some solutions for 3 X 2 with a(1,1)=0:
%e A184368 ..0..0....0..0....0..1....0..0....0..0....0..1....0..1....0..2....0..1....0..0
%e A184368 ..1..0....2..2....1..1....2..1....0..2....0..0....2..1....0..2....0..1....1..2
%e A184368 ..2..0....1..1....2..0....0..0....0..2....0..2....2..2....0..2....0..2....1..0
%Y A184368 Cf. A184376.
%K A184368 nonn
%O A184368 1,1
%A A184368 _R. H. Hardin_, Jan 12 2011