%I #8 Mar 01 2018 11:01:15
%S 2,6,13,34,81,199,487,1190,2910,7115,17398,42539,104013,254325,621854,
%T 1520506,3717817,9090502,22227349,54348491,132888475,324928002,
%U 794487306,1942615215,4749923434,11614123295,28397901945,69436221265,169779754602
%N Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,1,2,0,4 for x=0,1,2,3,4.
%C Every 0 is next to 0 3's, every 1 is next to 1 1's, every 2 is next to 2 2's, every 3 is next to 3 0's, every 4 is next to 4 4's.
%C Column 2 of A196912.
%H R. H. Hardin, <a href="/A196906/b196906.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = a(n-1) + 2*a(n-2) + 3*a(n-3) + 2*a(n-4) - a(n-6).
%F Empirical g.f.: x*(2 + 4*x + 3*x^2 + 3*x^3 - x^4 - x^5) / (1 - x - 2*x^2 - 3*x^3 - 2*x^4 + x^6). - _Colin Barker_, Mar 01 2018
%e Some solutions for n=4:
%e ..1..1....1..1....0..1....1..1....2..2....1..1....0..0....1..1....1..1....2..2
%e ..0..0....0..0....0..1....0..0....2..2....0..0....2..2....0..0....2..2....2..2
%e ..1..0....0..0....0..0....0..1....0..1....1..1....2..2....2..2....2..2....0..0
%e ..1..0....0..0....0..0....0..1....0..1....0..0....0..0....2..2....0..0....1..1
%Y Cf. A196912.
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 07 2011