%I A055165
%S A055165 1,6,174,22560,12514320,28836612000,270345669985440,
%T A055165 10160459763342013440
%N A055165 Number of regular n X n matrices with rational entries equal to 0 or 
               1.
%C A055165 All eigenvalues are nonzero.
%D A055165 Miodrag Zivkovic, Classification of small (0,1) matrices, Linear Algebra 
               and its Applications, 414 (2006), 310-346
%H A055165 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               NonsingularMatrix.html">Link to a section of The World of Mathematics.</
               a>
%H A055165 Miodrag Zivkovic, <a href="http://www.matf.bg.ac.yu/~ezivkovm/01matrices.htm">
               More information</a>
%H A055165 <a href="Sindx_Mat.html#binmat">Index entries for sequences related to 
               binary matrices</a>
%F A055165 For an asymptotic estimate see A046747. A002884 is a lower bound. A002416 
               is an upper bound.
%F A055165 a(n) = n! * A088389(n) - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), 
               Oct 20 2007
%e A055165 For n=2 the 6 matrices are {{{0, 1}, {1, 0}}, {{0, 1}, {1, 1}}, {{1, 
               0}, {0, 1}}, {{1, 0}, {1, 1}}, {{1, 1}, {0, 1}}, {{1, 1}, {1, 0}}}.
%Y A055165 Cf. A056990, A056989, A046747, A055165, A002416, A003024 (positive definite 
               matrices).
%Y A055165 A046747(n) + a(n) = 2^(n^2) = total number of n X n (0, 1) matrices = 
               sequence A002416.
%Y A055165 Sequence in context: A003720 A002884 A166762 this_sequence A071095 A134632 
               A024277
%Y A055165 Adjacent sequences: A055162 A055163 A055164 this_sequence A055166 A055167 
               A055168
%K A055165 nonn,nice,hard
%O A055165 1,2
%A A055165 Ulrich Hermisson (uhermiss(AT)server1.rz.uni-leipzig.de), Jun 18 2000
%E A055165 More terms from MIodrag Zivkovic (ezivkovm(AT)matf.bg.ac.yu), Feb 28 
               2006