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%I #8 Feb 22 2018 11:12:13
%S 2,5,11,34,101,299,890,2643,7855,23340,69355,206087,612384,1819689,
%T 5407175,16067330,47743801,141869903,421564034,1252670447,3722289195,
%U 11060719828,32866743207,97662975451,290203891328,862335989181
%N Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,3,0,4 for x=0,1,2,3,4.
%C Every 0 is next to 0 2's, every 1 is next to 1 1's, every 2 is next to 2 3's, every 3 is next to 3 0's, every 4 is next to 4 4's.
%C Column 2 of A196696.
%H R. H. Hardin, <a href="/A196690/b196690.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - a(n-4) for n>5.
%F Empirical g.f.: x*(2 + x - 5*x^2 - 3*x^3 + 2*x^4) / (1 - 2*x - 3*x^2 + x^4). - _Colin Barker_, Feb 22 2018
%e Some solutions for n=4:
%e ..0..0....0..0....0..0....0..1....1..1....0..0....0..0....1..1....1..1....0..0
%e ..0..3....1..1....0..3....0..1....0..0....0..0....3..0....0..0....0..0....0..0
%e ..0..0....0..0....3..0....0..0....0..0....0..3....0..0....0..1....3..0....1..0
%e ..1..1....0..0....0..0....1..1....1..1....0..0....0..0....0..1....0..0....1..0
%Y Cf. A196696.
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 05 2011
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