Search: id:A070322
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%I A070322
%S A070322 1,1,3,139,25575,18077431
%N A070322 Number of primitive n X n real (0,1)-matrices.
%C A070322 An n X n nonnegative matrix A is primitive iff every element of A^k is 
               > 0 for some power k. If A is primitive then the power which should 
               have all positive entries is <= n^2 - 2n + 2 (Wielandt).
%D A070322 Sachkov, V. N. and Tarakanov, V. E., Combinatorics of Nonnegative Matrices. 
               Translations of Mathematical Monographs, 213. American Mathematical 
               Society, Providence, RI, 2002.
%D A070322 Wielandt, H. 1950. Unzerlegbare nicht negativen Matrizen, Math. Z. 52, 
               642-648.
%H A070322 S. J. Leon, <a href="http://www.prenhall.com/divisions/esm/app/ph-linear/
               leon/html/perron.html">Linear Algebra with Applications: THE PERRON-FROBENIUS 
               THEOREM</a>
%H A070322 <a href="Sindx_Mat.html#binmat">Index entries for sequences related to 
               binary matrices</a>
%F A070322 For asymptotics see Sachkov and Tarakanov.
%t A070322 Table[ it=Partition[ #, n ]&/@IntegerDigits[ Range[ 0, -1+2^n^2 ], 2, 
               n^2 ]; Count [ it, (q_?MatrixQ) /; (Max@@Table[ Min@@Flatten[ MatrixPower[ 
               q, k ] ], {k, 1, n^2-2n+2} ] )>0 ], {n, 1, 4} ]
%Y A070322 Sequence in context: A030247 A139956 A016067 this_sequence A053527 A152504 
               A035331
%Y A070322 Adjacent sequences: A070319 A070320 A070321 this_sequence A070323 A070324 
               A070325
%K A070322 nonn
%O A070322 0,3
%A A070322 N. J. A. Sloane (njas(AT)research.att.com), Aug 22 2003
%E A070322 Wouter Meeussen (wouter.meeussen(AT)pandora.be) computed a(0) through 
               a(4), Aug 22, 2003.
%E A070322 Jack Kennedy (kennedy(AT)oldnews.org) computed a(0) through a(5), Aug 
               22, 2003.

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