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A196012 Number of n X 3 0..4 arrays with each element equal to the number its horizontal and vertical neighbors within one of itself.

%I A196012 #9 May 08 2018 06:19:43
%S A196012 1,1,2,7,13,16,32,65,125,211,390,732,1368,2478,4555,8417,15564,28583,
%T A196012 52598,96921,178684,328956,605723,1115678,2055336,3785356,6971537,
%U A196012 12840292,23650713,43560381,80229677,147768685,272167135,501285666
%N A196012 Number of n X 3 0..4 arrays with each element equal to the number its horizontal and vertical neighbors within one of itself.
%C A196012 Column 3 of A196017.
%H A196012 R. H. Hardin, <a href="/A196012/b196012.txt">Table of n, a(n) for n = 1..200</a>
%F A196012 Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-4) -a(n-5) -2*a(n-6).
%F A196012 Empirical g.f.: x*(1 - x)*(1 + x + x^2 + 5*x^3 + 6*x^4) / (1 - x - x^2 - 3*x^4 + x^5 + 2*x^6). - _Colin Barker_, May 08 2018
%e A196012 All solutions for n=4:
%e A196012 ..2..2..0....2..2..2....0..2..2....2..3..2....2..2..2....2..3..2....2..2..2
%e A196012 ..3..3..2....2..0..2....2..3..3....3..4..3....2..0..2....3..3..3....2..0..2
%e A196012 ..2..0..2....3..3..3....2..0..2....3..4..3....2..3..3....2..0..2....3..3..2
%e A196012 ..2..2..2....2..3..2....2..2..2....2..3..2....0..2..2....2..2..2....2..2..0
%Y A196012 Cf. A196017.
%K A196012 nonn
%O A196012 1,3
%A A196012 _R. H. Hardin_, Sep 26 2011