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%I #8 Jun 07 2018 11:47:13
%S 8,42,256,1682,11448,79162,551216,3849762,26922088,188375882,
%T 1318394976,9228056242,64594267928,452153498202,3165055355536,
%U 22155330093122,155087138464968,1085609452694122,7599264619176896,53194847685192402
%N Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..3 introduced in row major order.
%C Column 1 of A204572.
%H R. H. Hardin, <a href="/A204565/b204565.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 11*a(n-1) - 31*a(n-2) + 21*a(n-3).
%F Conjectures from _Colin Barker_, Jun 07 2018: (Start)
%F G.f.: 2*x*(4 - 23*x + 21*x^2) / ((1 - x)*(1 - 3*x)*(1 - 7*x)).
%F a(n) = 1/3 + 3^n + (2*7^n)/3.
%F (End)
%e Some solutions for n=4:
%e ..0..0....0..0....0..0....0..0....0..0....0..1....0..1....0..0....0..1....0..0
%e ..1..0....0..0....0..0....0..0....0..0....0..0....1..0....0..0....1..0....0..0
%e ..0..1....0..0....0..0....0..0....0..1....0..0....0..0....0..0....0..0....1..0
%e ..1..0....0..1....0..1....1..0....1..1....1..0....0..1....0..0....2..0....2..1
%e ..0..0....1..2....1..0....1..1....0..1....2..1....0..0....0..0....0..2....2..2
%Y Cf. A204572.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 16 2012
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