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A196488 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,3,0,1,4 for x=0,1,2,3,4.

%I A196488 #8 May 09 2018 08:16:53
%S A196488 1,3,9,23,69,199,553,1563,4439,12591,35645,100885,285753,809481,
%T A196488 2292615,6492777,18388691,52081399,147506079,417765845,1183196095,
%U A196488 3351057703,9490892585,26880156625,76130113051,215616141961,610669320471
%N A196488 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,3,0,1,4 for x=0,1,2,3,4.
%C A196488 Every 0 is next to 0 2's, every 1 is next to 1 3's, every 2 is next to 2 0's, every 3 is next to 3 1's, every 4 is next to 4 4's.
%C A196488 Column 3 of A196493.
%H A196488 R. H. Hardin, <a href="/A196488/b196488.txt">Table of n, a(n) for n = 1..200</a>
%F A196488 Empirical: a(n) = a(n-1) +a(n-2) +6*a(n-3) +10*a(n-4) +15*a(n-5) +9*a(n-6) +4*a(n-7) +a(n-8).
%F A196488 Empirical g.f.: x*(1 + 2*x + 5*x^2 + 5*x^3 + 9*x^4 + 8*x^5 + 3*x^6 + x^7) / (1 - x - x^2 - 6*x^3 - 10*x^4 - 15*x^5 - 9*x^6 - 4*x^7 - x^8). - _Colin Barker_, May 09 2018
%e A196488 Some solutions for n=4:
%e A196488 ..0..0..0....0..0..0....0..0..0....1..0..0....1..3..1....0..1..0....1..3..1
%e A196488 ..0..1..0....0..0..0....0..1..0....3..1..1....1..1..0....0..3..1....0..1..1
%e A196488 ..1..3..1....1..3..1....1..3..0....1..1..3....3..1..0....0..1..0....0..1..3
%e A196488 ..0..0..0....0..1..0....0..1..0....0..0..1....1..0..0....0..0..0....0..0..1
%Y A196488 Cf. A196493.
%K A196488 nonn
%O A196488 1,2
%A A196488 _R. H. Hardin_, Oct 03 2011