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A197469 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,0,0,0 for x=0,1,2,3,4.

%I A197469 #8 May 12 2018 14:36:03
%S A197469 1,2,6,12,24,50,98,194,394,786,1562,3138,6282,12530,25082,50210,
%T A197469 100330,200658,401498,802818,1605450,3211442,6422714,12844514,
%U A197469 25690282,51381138,102759194,205520322,411044874,822081650,1644162938,3288342434
%N A197469 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,0,0,0 for x=0,1,2,3,4.
%C A197469 Every 0 is next to 0 0's, every 1 is next to 1 1's, every 2 is next to 2 0's, every 3 is next to 3 0's, every 4 is next to 4 0's.
%C A197469 Column 2 of A197475.
%H A197469 R. H. Hardin, <a href="/A197469/b197469.txt">Table of n, a(n) for n = 1..200</a>
%F A197469 Empirical: a(n) = a(n-1) +4*a(n-3) for n>6.
%F A197469 Empirical g.f.: x*(1 + x + 4*x^2 + 2*x^3 + 4*x^4 + 2*x^5) / ((1 - 2*x)*(1 + x + 2*x^2)). - _Colin Barker_, May 12 2018
%e A197469 Some solutions for n=4:
%e A197469 ..1..1....1..1....0..1....1..1....2..0....2..0....0..2....1..0....2..0....0..2
%e A197469 ..2..0....0..2....2..1....0..2....0..3....0..2....3..0....1..2....0..3....2..0
%e A197469 ..0..2....3..0....0..2....2..0....3..0....2..1....0..2....2..0....2..0....1..2
%e A197469 ..1..1....0..2....2..0....1..1....0..2....0..1....1..1....0..2....1..1....1..0
%Y A197469 Cf. A197475.
%K A197469 nonn
%O A197469 1,2
%A A197469 _R. H. Hardin_, Oct 15 2011