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%I #10 Mar 27 2018 08:48:45
%S 1,2,11,44,188,752,3056,12224,49088,196352,786176,3144704,12581888,
%T 50327552,201322496,805289984,3221209088,12884836352,51539542016,
%U 206158168064,824633458688,3298533834752,13194138484736,52776553938944
%N Number of 2 X n binary matrices M with rows in strictly increasing order and rows of M*Mtranspose (mod 2) in strictly increasing order.
%C Row 2 of A181266.
%H R. H. Hardin, <a href="/A181270/b181270.txt">Table of n, a(n) for n=1..200</a>
%F Empirical (for n>=2): 3*4^(n-2) - (3+(-1)^n)*2^(n-4). - _Vaclav Kotesovec_, Nov 27 2012
%F Conjectures from _Colin Barker_, Mar 27 2018: (Start)
%F G.f.: x*(1 - 2*x - x^2 + 8*x^3) / ((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>4.
%F (End)
%e M and M*Mtranspose (mod 2) for 2 X 3:
%e ..0..1..1......0..1
%e ..1..0..1......1..0
%Y Cf. A181266.
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 10 2010
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