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A204624 Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

%I A204624 #8 Jun 07 2018 14:25:52
%S A204624 96,2049,43734,933462,19923888,425257068,9076721064,193734264456,
%T A204624 4135079723136,88259474206608,1883817316421472,40208348322379872,
%U A204624 858210220662456576,18317707978060726464,390974632428061590144
%N A204624 Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.
%C A204624 Column 2 of A204630.
%H A204624 R. H. Hardin, <a href="/A204624/b204624.txt">Table of n, a(n) for n = 1..210</a>
%F A204624 Empirical: a(n) = 22*a(n-1) -14*a(n-2).
%F A204624 Conjectures from _Colin Barker_, Jun 07 2018: (Start)
%F A204624 G.f.: 3*x*(32 - 21*x) / (1 - 22*x + 14*x^2).
%F A204624 a(n) = (3*(11+sqrt(107))^n*(31+3*sqrt(107)) + (11-sqrt(107))^n*(-93+9*sqrt(107))) / (4*sqrt(107)).
%F A204624 (End)
%e A204624 Some solutions for n=3:
%e A204624 ..0..0..0....0..0..1....0..0..1....0..1..2....0..0..1....0..0..1....0..1..0
%e A204624 ..0..1..1....2..0..2....2..0..2....1..2..2....2..0..0....2..0..2....2..1..2
%e A204624 ..1..2..0....0..0..2....2..2..1....0..2..1....2..0..1....1..0..2....2..1..1
%e A204624 ..1..2..1....2..0..2....0..2..1....1..1..0....2..2..2....1..2..1....0..1..2
%Y A204624 Cf. A204630.
%K A204624 nonn
%O A204624 1,1
%A A204624 _R. H. Hardin_, Jan 17 2012