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%I #12 Mar 03 2018 13:52:26
%S 13,159,2277,33831,506493,7594479,113908437,1708600311,25628925933,
%T 384433652799,5766504083397,86497559125191,1297463380500573,
%U 19461950688376719,291929260268255157,4378938903851640471
%N Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..3 introduced in row major order.
%C Column 1 of A205170.
%H R. H. Hardin, <a href="/A205163/b205163.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 18*a(n-1) - 45*a(n-2).
%F Conjectures from _Colin Barker_, Mar 03 2018: (Start)
%F G.f.: x*(13 - 75*x) / ((1 - 3*x)*(1 - 15*x)).
%F a(n) = 3^(n-1)*(2*5^n+3).
%F (End)
%e Some solutions for n=4:
%e 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
%e 0 1 1 1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1
%e 0 0 0 0 0 2 0 2 1 2 0 2 2 0 1 2 2 0 0 0
%e 0 1 0 1 1 3 1 3 1 3 2 1 3 1 0 1 0 1 1 0
%e 1 1 0 0 0 1 2 0 0 0 1 0 1 2 0 0 3 0 2 3
%Y Cf. A205170.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 22 2012
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