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%I #13 Feb 20 2018 07:38:48
%S 16,47,125,335,907,2470,6740,18406,50278,137354,375250,1025194,
%T 2800874,7652122,20905978,57116186,156044314,426320986,1164730586,
%U 3182103130,8693667418,23751541082,64890416986,177283916122,484348666202
%N Number of (n+1) X 2 0..1 arrays with the determinants of 2 X 2 subblocks nondecreasing rightwards and downwards.
%C Column 1 of A204616.
%H R. H. Hardin, <a href="/A204609/b204609.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) - 2*a(n-3) for n>6.
%F Conjectures from _Colin Barker_, Feb 20 2018: (Start)
%F G.f.: (16 - x - 16*x^2 - 8*x^3 - 4*x^4 - x^5) / ((1 - x)*(1 - 2*x - 2*x^2)).
%F a(n) = (112 + (193-113*sqrt(3))*(1-sqrt(3))^n + (1+sqrt(3))^n*(193+113*sqrt(3))) / 24 for n>2.
%F (End)
%e Some solutions for n=4:
%e ..1..1....1..0....0..0....0..0....1..1....1..1....1..0....1..0....0..0....1..1
%e ..1..1....0..0....1..0....0..1....0..0....0..0....0..0....0..0....0..1....1..1
%e ..1..1....0..1....0..0....0..0....0..0....0..0....1..0....0..1....0..1....1..1
%e ..0..0....0..1....0..1....1..0....0..1....1..1....1..1....0..1....0..1....1..1
%e ..1..1....0..0....0..1....1..0....0..1....1..1....0..1....0..1....0..1....1..1
%Y Cf. A204616.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 17 2012
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