%I
%S 1,5,14,43,124,352,1025,2977,8619,24982,72411,209844,608174,1762633,
%T 5108427,14805217,42908476,124357153,360411436,1044543248,3027291501,
%U 8773685473,25427864489,73694947188,213582435997,619003863520
%N Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,2,1,1,1 for x=0,1,2,3,4.
%C Every 0 is next to 0 4's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's.
%C Column 2 of A197613.
%H R. H. Hardin, <a href="/A197607/b197607.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 2*a(n1) + a(n2) + 4*a(n3) + a(n4) + 2*a(n5) + 2*a(n6)  a(n7)  a(n8).
%F Empirical g.f.: x*(1 + x)*(1 + 2*x + x^2 + 5*x^3  2*x^4  x^6) / (1  2*x  x^2  4*x^3  x^4  2*x^5  2*x^6 + x^7 + x^8).  _Colin Barker_, Mar 02 2018
%e Some solutions for n=4:
%e ..1..0....0..0....0..0....1..2....0..0....1..2....2..1....0..1....0..0....1..2
%e ..2..1....1..0....0..0....0..1....2..1....3..1....1..3....1..2....2..1....0..1
%e ..0..1....2..0....2..1....2..1....1..0....1..0....0..1....0..0....1..1....1..0
%e ..1..2....1..0....1..0....1..0....0..0....2..1....1..2....0..0....1..2....2..1
%Y Cf. A197613.
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 16 2011
