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%I #10 Mar 27 2018 09:36:26
%S 0,0,6,87,730,6236,49400,398032,3162528,25293504,201794944,1613449472,
%T 12895556096,103137221632,824854591488,6598199365632,52780897705984,
%U 422233760645120,3377782040133632,27021990036570112,216174305392852992
%N Number of 3 X n binary matrices M with rows in strictly increasing order and rows of M*Mtranspose (mod 2) in strictly increasing order.
%C Row 3 of A181266.
%H R. H. Hardin, <a href="/A181271/b181271.txt">Table of n, a(n) for n=1..146</a>
%F Empirical (for n>=3): 3*2^(3*n-7) + (18*n - 99 + 13*(-1)^n)*4^(n-4)/3 - (6*n - 1 + 3*(-1)^n)*2^(n-5)/3. - _Vaclav Kotesovec_, Nov 27 2012
%F Conjectures from _Colin Barker_, Mar 27 2018: (Start)
%F G.f.: x^3*(6 + 3*x - 272*x^2 + 444*x^3 + 832*x^4 - 960*x^5 - 512*x^6) / ((1 - 2*x)^2*(1 + 2*x)*(1 - 4*x)^2*(1 + 4*x)*(1 - 8*x)).
%F a(n) = 14*a(n-1) - 36*a(n-2) - 216*a(n-3) + 1056*a(n-4) - 384*a(n-5) - 3584*a(n-6) + 4096*a(n-7) for n>9.
%F (End)
%e M and M*Mtranspose (mod 2) for 3 X 3:
%e ..0..1..1......0..0..1
%e ..1..0..0......0..1..1
%e ..1..0..1......1..1..0
%Y Cf. A181266.
%K nonn
%O 1,3
%A _R. H. Hardin_, Oct 10 2010