%I
%S 21,153,1107,8019,58077,420633,3046491,22064643,159806277,1157419449,
%T 8382773187,60713414163,439725443661,3184773389433,23066169329547,
%U 167059976482179,1209955382858997,8763272085493593,63469230958692531
%N 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 Column 1 of A184376.
%H R. H. Hardin, <a href="/A184368/b184368.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 6*a(n1) + 9*a(n2).
%F Conjectures from _Colin Barker_, Feb 27 2018: (Start)
%F G.f.: 3*x*(7 + 9*x) / (1  6*x  9*x^2).
%F a(n) = ((33*sqrt(2))^n*(4+3*sqrt(2)) + (3*(1+sqrt(2)))^n*(4+3*sqrt(2))) / (2*sqrt(2)).
%F (End)
%e Some solutions for 3 X 2 with a(1,1)=0:
%e ..0..0....0..0....0..1....0..0....0..0....0..1....0..1....0..2....0..1....0..0
%e ..1..0....2..2....1..1....2..1....0..2....0..0....2..1....0..2....0..1....1..2
%e ..2..0....1..1....2..0....0..0....0..2....0..2....2..2....0..2....0..2....1..0
%Y Cf. A184376.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 12 2011
