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A197444 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,1,0,0 for x=0,1,2,3,4.

%I A197444 #8 May 12 2018 14:36:38
%S A197444 2,5,12,36,107,321,957,2868,8581,25694,76914,230273,689377,2063867,
%T A197444 6178778,18498023,55379290,165794354,496354537,1485984549,4448735449,
%U A197444 13318609060,39873206463,119372269782,357376295102,1069911935955
%N A197444 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,1,0,0 for x=0,1,2,3,4.
%C A197444 Every 0 is next to 0 2's, every 1 is next to 1 1's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 0's.
%C A197444 Column 2 of A197450.
%H A197444 R. H. Hardin, <a href="/A197444/b197444.txt">Table of n, a(n) for n = 1..200</a>
%F A197444 Empirical: a(n) = 2*a(n-1) +5*a(n-2) -4*a(n-3) -6*a(n-4) -a(n-5) +4*a(n-7) +a(n-8).
%F A197444 Empirical g.f.: x*(2 + x - 8*x^2 - 5*x^3 + 7*x^4 + 7*x^5 + x^6 - 3*x^7) / ((1 - x)*(1 - x - 6*x^2 - 2*x^3 + 4*x^4 + 5*x^5 + 5*x^6 + x^7)). - _Colin Barker_, May 12 2018
%e A197444 Some solutions for n=4:
%e A197444 ..0..0....0..0....0..0....1..1....0..0....0..0....0..0....0..0....0..1....1..0
%e A197444 ..1..1....1..1....1..0....0..0....1..1....0..0....0..3....0..0....0..1....1..0
%e A197444 ..0..0....0..0....1..0....0..3....2..2....0..3....1..0....3..0....1..0....0..0
%e A197444 ..1..1....0..0....0..0....0..0....1..1....0..0....1..0....0..0....1..0....0..0
%Y A197444 Cf. A197450.
%K A197444 nonn
%O A197444 1,1
%A A197444 _R. H. Hardin_, Oct 15 2011