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

%I #9 May 09 2018 15:55:51

%S 1,3,7,12,27,58,121,257,545,1153,2442,5172,10952,23193,49116,104012,

%T 220265,466453,987802,2091857,4429902,9381153,19866361,42070767,

%U 89092785,188670778,399545962,846113942,1791805877,3794486938,8035541856

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

%C Every 0 is next to 0 1's, every 1 is next to 1 3's, every 2 is next to 2 2's, every 3 is next to 3 4's, every 4 is next to 4 0's.

%C Column 3 of A196922.

%H R. H. Hardin, <a href="/A196917/b196917.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) +a(n-3) -a(n-4) for n>5.

%F Empirical g.f.: x*(1 + x + x^2 - 3*x^3 + x^4) / (1 - 2*x - x^3 + x^4). - _Colin Barker_, May 09 2018

%e Some solutions for n=4:

%e ..0..0..0....0..2..2....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0

%e ..2..2..2....0..2..2....0..0..0....2..2..0....0..0..0....0..0..0....0..0..0

%e ..2..0..2....0..0..0....0..2..2....2..2..0....2..2..0....0..4..0....0..0..0

%e ..2..2..2....0..0..0....0..2..2....0..0..0....2..2..0....0..0..0....0..0..0

%Y Cf. A196922.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 07 2011