%I
%S 0,4,3,8,14,19,46,56,133,184,372,599,1064,1874,3147,5692,9516,17053,
%T 28980,51004,88089,153086,266660,461205,804810,1392380,2426083,
%U 4205680,7313450,12699273,22056242,38328650,66544359,115648570,200804584
%N Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,3,4 for x=0,1,2,3,4.
%C Every 0 is next to 0 0's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 3's, every 4 is next to 4 4's.
%C Column 2 of A196138.
%H R. H. Hardin, <a href="/A196132/b196132.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 3*a(n2) +2*a(n3) 2*a(n4) 3*a(n5) a(n6) +4*a(n7) 2*a(n9).
%F Empirical g.f.: x^2*(4 + 3*x  4*x^2  3*x^3  3*x^4 + 6*x^5  4*x^7) / ((1  x)*(1 + x  2*x^2  4*x^3  2*x^4 + x^5 + 2*x^6  2*x^7  2*x^8)).  _Colin Barker_, May 08 2018
%e All solutions for n=4:
%e ..0..1....2..1....1..2....2..1....1..0....0..1....1..0....1..2
%e ..1..2....1..0....0..1....1..0....2..1....1..2....2..1....0..1
%e ..1..0....0..1....2..1....1..2....0..1....1..2....2..1....1..0
%e ..2..1....1..2....1..0....0..1....1..2....0..1....1..0....2..1
%Y Cf. A196138.
%K nonn
%O 1,2
%A _R. H. Hardin_, Sep 28 2011
