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A196431 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,0,3,4 for x=0,1,2,3,4.

%I A196431 #9 Mar 01 2018 05:47:20
%S A196431 3,9,25,75,213,621,1801,5219,15133,43867,127195,368759,1069105,
%T A196431 3099583,8986391,26053581,75535111,218993223,634910491,1840747761,
%U A196431 5336740123,15472405305,44857970049,130053306249,377053674603,1093163086545
%N A196431 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,0,3,4 for x=0,1,2,3,4.
%C A196431 Every 0 is next to 0 2's, every 1 is next to 1 1's, every 2 is next to 2 0's, every 3 is next to 3 3's, every 4 is next to 4 4's.
%C A196431 Column 3 of A196436.
%H A196431 R. H. Hardin, <a href="/A196431/b196431.txt">Table of n, a(n) for n = 1..200</a>
%F A196431 Empirical: a(n) = a(n-1) + 3*a(n-2) + 5*a(n-3) + 6*a(n-4) + 4*a(n-5) - 5*a(n-6) - 5*a(n-7) - a(n-8) + a(n-9).
%F A196431 Empirical g.f.: x*(1 + x)*(3 + 3*x + 4*x^2 + 4*x^3 - 4*x^4 - 4*x^5 - x^6 + x^7) / (1 - x - 3*x^2 - 5*x^3 - 6*x^4 - 4*x^5 + 5*x^6 + 5*x^7 + x^8 - x^9). - _Colin Barker_, Mar 01 2018
%e A196431 Some solutions for n=4:
%e A196431 ..0..0..0....1..1..0....1..1..0....0..1..1....0..1..0....1..1..0....0..0..0
%e A196431 ..0..0..0....0..0..1....0..0..0....1..0..0....0..1..0....0..0..0....0..1..1
%e A196431 ..1..0..0....0..0..1....0..0..1....1..0..1....1..0..1....1..0..1....0..0..0
%e A196431 ..1..0..0....0..0..0....0..0..1....0..0..1....1..0..1....1..0..1....0..0..0
%Y A196431 Cf. A196436.
%K A196431 nonn
%O A196431 1,1
%A A196431 _R. H. Hardin_, Oct 02 2011