%I #9 May 15 2018 06:42:06

%S 4,36,376,3936,41216,431616,4519936,47333376,495681536,5190844416,

%T 54359228416,569257230336,5961339109376,62427953627136,

%U 653754017775616,6846200955273216,71694347178868736,750792950862053376

%N Number of 2n X 2 0..2 arrays with values 0..2 introduced in row major order and each element equal to an even number of horizontal and vertical neighbors.

%C Column 1 of A198642.

%H R. H. Hardin, <a href="/A198638/b198638.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 12*a(n-1) -16*a(n-2) for n>3.

%F Conjectures from _Colin Barker_, May 15 2018: (Start)

%F G.f.: 4*x*(1 - x)*(1 - 2*x) / (1 - 12*x + 16*x^2).

%F a(n) = ((6 - 2*sqrt(5))^n*(-5+3*sqrt(5)) + (2*(3+sqrt(5)))^n*(5+3*sqrt(5))) / (16*sqrt(5)) for n>1.

%F (End)

%e Some solutions for n=3:

%e ..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1

%e ..1..0....1..2....1..0....1..2....2..0....2..0....1..0....2..0....1..2....2..0

%e ..0..2....2..0....2..1....0..1....0..1....0..1....2..1....1..2....0..1....1..2

%e ..2..0....0..2....0..2....2..2....1..2....1..2....1..2....2..1....1..2....0..1

%e ..1..1....2..0....2..0....2..2....2..0....2..1....0..1....0..2....2..1....1..0

%e ..1..1....1..2....0..2....1..0....0..1....1..2....2..0....2..0....0..2....0..2

%Y Cf. A198642.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 27 2011