%I #8 Apr 12 2018 06:31:51
%S 43,499,5695,65227,746503,8544883,97806031,1119511003,12814167895,
%T 146673819139,1678861073311,19216616595691,219957659413927,
%U 2517684199404691,28817972258232175,329856907907420923
%N 1/4 the number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having at least two equal elements connected horizontally or vertically.
%C Column 1 of A184153.
%H R. H. Hardin, <a href="/A184145/b184145.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 9*a(n1) + 28*a(n2).
%F Conjectures from _Colin Barker_, Apr 12 2018: (Start)
%F G.f.: x*(43 + 112*x) / (1  9*x  28*x^2).
%F a(n) = (2^(n)*((9sqrt(193))^n*(25+2*sqrt(193)) + (9+sqrt(193))^n*(25+2*sqrt(193)))) / sqrt(193).
%F (End)
%e Some solutions for 3 X 2 with a(1,1)=0:
%e ..0..2....0..2....0..0....0..0....0..1....0..0....0..2....0..2....0..0....0..0
%e ..3..2....1..1....2..0....1..1....0..2....0..3....1..1....0..0....1..2....0..0
%e ..0..2....2..3....0..0....1..0....3..2....1..1....3..2....0..3....1..2....0..2
%Y Cf. A184153.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 09 2011
