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%I #11 Mar 27 2018 09:36:37
%S 0,0,9,79,766,6060,49928,395024,3170784,25244608,201926272,1612664064,
%T 12897654272,103124642816,824888150016,6597998055424,52781434593280,
%U 422230539485184,3377790630133760,27021938497224704,216174442832068608
%N Number of 3 X n binary matrices M with rows in strictly increasing order and rows of M*Mtranspose (mod 2) in strictly decreasing order.
%C Row 3 of A181274.
%H R. H. Hardin, <a href="/A181279/b181279.txt">Table of n, a(n) for n=1..144</a>
%F Empirical (for n>=3): 3*2^(3*n-7) + (18*n - 105 - 17*(-1)^n)*4^(n-4)/3 - (6*n - 19 - 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*(9 - 47*x - 16*x^2 + 124*x^3 + 224*x^4 - 320*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..0......1..1..0
%e ..0..1..1......1..0..0
%e ..1..0..0......0..0..1
%Y Cf. A181274.
%K nonn
%O 1,3
%A _R. H. Hardin_, Oct 10 2010
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