%I #8 Jun 02 2018 10:35:11

%S 1,4,14,40,116,344,1016,2992,8816,25984,76576,225664,665024,1959808,

%T 5775488,17020160,50157824,147813376,435600896,1283700736,3783021568,

%U 11148433408,32854046720,96819736576,285324406784,840841134080

%N Number of n X 2 0..1 arrays with every one equal to some NW, E or S neighbor.

%C Column 2 of A202906.

%H R. H. Hardin, <a href="/A202900/b202900.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) -4*a(n-2) +4*a(n-3) -4*a(n-4).

%F Empirical g.f.: x*(1 + 2*x^2 - 4*x^3) / (1 - 4*x + 4*x^2 - 4*x^3 + 4*x^4). - _Colin Barker_, Jun 02 2018

%e Some solutions for n=5:

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

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

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

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

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

%Y Cf. A202906.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 25 2011