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A204070 Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.

%I A204070 #8 Jun 06 2018 05:41:04
%S A204070 38,329,2882,25277,221726,1944977,17061338,149662085,1312836086,
%T A204070 11516200601,101020133234,886148797901,7773298914638,68187392635937,
%U A204070 598139935894154,5246884637775509,46025681868191270,403737367538170409
%N A204070 Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.
%C A204070 Column 2 of A204076.
%H A204070 R. H. Hardin, <a href="/A204070/b204070.txt">Table of n, a(n) for n = 1..210</a>
%F A204070 Empirical: a(n) = 10*a(n-1) - 11*a(n-2) + 2*a(n-3).
%F A204070 Conjectures from _Colin Barker_, Jun 06 2018: (Start)
%F A204070 G.f.: x*(38 - 51*x + 10*x^2) / ((1 - x)*(1 - 9*x + 2*x^2)).
%F A204070 a(n) = 1/2 + (2^(-2-n)*(3*(9+sqrt(73))^n*(23+3*sqrt(73)) + (9-sqrt(73))^n*(-69+9*sqrt(73)))) / sqrt(73).
%F A204070 (End)
%e A204070 Some solutions for n=4:
%e A204070 ..0..1..0....0..0..0....0..0..0....0..1..2....0..0..0....0..0..1....0..0..1
%e A204070 ..0..0..1....0..1..0....0..1..0....1..1..1....1..0..1....1..0..0....2..0..0
%e A204070 ..1..0..0....2..0..1....0..0..2....1..1..1....2..1..2....1..1..0....1..2..0
%e A204070 ..1..1..0....2..2..0....1..0..0....0..1..2....0..2..2....2..1..1....1..1..2
%e A204070 ..2..1..1....0..2..2....2..1..0....2..0..1....2..0..2....0..2..1....2..1..1
%Y A204070 Cf. A204076.
%K A204070 nonn
%O A204070 1,1
%A A204070 _R. H. Hardin_, Jan 10 2012