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%I #9 May 10 2018 11:26:46
%S 2,6,15,48,145,449,1397,4342,13500,41981,130562,406025,1262695,
%T 3926857,12212128,37978464,118109177,367307576,1142289291,3552403843,
%U 11047615721,34356964532,106846675430,332282325069,1033364333556,3213658281627
%N Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,1,2,0,3 for x=0,1,2,3,4.
%C Every 0 is next to 0 4's, every 1 is next to 1 1's, every 2 is next to 2 2's, every 3 is next to 3 0's, every 4 is next to 4 3's.
%C Column 2 of A196967.
%H R. H. Hardin, <a href="/A196961/b196961.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 2*a(n-1) +3*a(n-2) +2*a(n-3) -5*a(n-5) -3*a(n-6) +2*a(n-7).
%F Empirical g.f.: x*(2 + 2*x - 3*x^2 - 4*x^3 - 8*x^4 - 5*x^5 + 4*x^6) / ((1 - x)*(1 - x - 4*x^2 - 6*x^3 - 6*x^4 - x^5 + 2*x^6)). - _Colin Barker_, May 10 2018
%e Some solutions for n=4:
%e ..0..1....2..2....0..0....0..0....0..0....0..0....2..2....0..0....1..0....0..0
%e ..0..1....2..2....2..2....3..0....0..0....3..0....2..2....0..0....1..0....0..3
%e ..0..0....0..1....2..2....0..3....2..2....0..1....0..0....1..1....2..2....0..0
%e ..0..0....0..1....1..1....0..0....2..2....0..1....1..1....0..0....2..2....0..0
%Y Cf. A196967.
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 08 2011
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