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%I #9 Feb 27 2018 07:11:10
%S 12,32,80,208,528,1360,3472,8912,22800,58448,149648,383440,982032,
%T 2515792,6443920,16507088,42282768,108311120,277442192,710686672,
%U 1820455440,4663202128,11945023888,30597832400,78377927952,200769257552
%N Number of (n+1) X 3 binary arrays with every 2 X 2 subblock nonsingular.
%C Column 2 of A183688.
%H R. H. Hardin, <a href="/A183682/b183682.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = a(n-1) + 4*a(n-2).
%F Conjectures from _Colin Barker_, Feb 27 2018: (Start)
%F G.f.: 4*x*(3 + 5*x) / (1 - x - 4*x^2).
%F a(n) = (2^(-1-n)*((1-sqrt(17))^n*(-19+5*sqrt(17)) + (1+sqrt(17))^n*(19+5*sqrt(17)))) / sqrt(17).
%F (End)
%e Some solutions for 5 X 3:
%e ..0..1..1....0..1..1....0..1..0....1..1..1....1..1..0....1..1..0....1..0..1
%e ..1..0..1....1..0..1....1..0..1....1..0..1....1..0..1....1..0..1....1..1..0
%e ..1..1..0....0..1..0....0..1..0....1..1..0....1..1..1....0..1..1....0..1..1
%e ..0..1..1....1..0..1....1..0..1....1..0..1....0..1..0....1..0..1....1..1..0
%e ..1..1..0....0..1..0....0..1..0....0..1..0....1..1..1....1..1..0....1..0..1
%Y Cf. A183688.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 06 2011