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A203829 Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.

%I A203829 #8 Jun 05 2018 11:17:52
%S A203829 225,1971,17289,151659,1330353,11669859,102368025,897972507,
%T A203829 7877016513,69097203603,606120799401,5316892787403,46639793487825,
%U A203829 409124355815619,3588839615364921,31481307826653051,276154091209147617
%N A203829 Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.
%C A203829 Column 2 of A203835.
%H A203829 R. H. Hardin, <a href="/A203829/b203829.txt">Table of n, a(n) for n = 1..210</a>
%F A203829 Empirical: a(n) = 9*a(n-1) -2*a(n-2).
%F A203829 Conjectures from _Colin Barker_, Jun 05 2018: (Start)
%F A203829 G.f.: 9*x*(25 - 6*x) / (1 - 9*x + 2*x^2).
%F A203829 a(n) = (9*2^(-1-n)*((9-sqrt(73))^n*(-23+3*sqrt(73)) + (9+sqrt(73))^n*(23+3*sqrt(73)))) / sqrt(73).
%F A203829 (End)
%e A203829 Some solutions for n=4:
%e A203829 ..1..1..2....0..0..2....2..1..0....0..0..2....1..1..2....2..2..2....2..0..1
%e A203829 ..0..1..1....0..0..0....0..2..1....0..0..0....1..1..1....1..2..0....0..0..0
%e A203829 ..2..0..1....0..1..0....1..0..2....1..0..0....1..1..1....2..2..2....2..0..1
%e A203829 ..1..2..0....0..0..1....1..1..0....1..1..0....0..1..2....1..2..1....2..2..0
%e A203829 ..0..1..2....0..2..0....2..1..1....0..1..1....2..0..1....2..0..2....2..0..0
%Y A203829 Cf. A203835.
%K A203829 nonn
%O A203829 1,1
%A A203829 _R. H. Hardin_, Jan 06 2012