%I #10 Mar 27 2018 08:49:24
%S 0,3,11,48,188,768,3056,12288,49088,196608,786176,3145728,12581888,
%T 50331648,201322496,805306368,3221209088,12884901888,51539542016,
%U 206158430208,824633458688,3298534883328,13194138484736,52776558133248
%N Number of 2 X n binary matrices M with rows in strictly increasing order and rows of M*Mtranspose (mod 2) in strictly decreasing order.
%C Row 2 of A181274.
%H R. H. Hardin, <a href="/A181278/b181278.txt">Table of n, a(n) for n=1..200</a>
%F Empirical (for n>=2): 3*4^(n-2) + ((-1)^n-1)*2^(n-4). - _Vaclav Kotesovec_, Nov 27 2012
%F Conjectures from _Colin Barker_, Mar 27 2018: (Start)
%F G.f.: x^2*(3 - x - 8*x^2) / ((1 - 2*x)*(1 + 2*x)*(1 - 4*x)).
%F a(n) = 4*a(n-1) + 4*a(n-2) - 16*a(n-3) for n>3.
%F (End)
%e M and M*Mtranspose (mod 2) for 2 X 3:
%e ..0..1..0......1..1
%e ..0..1..1......1..0
%Y Cf. A181274.
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 10 2010
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