Search: id:A055548
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%I A055548
%S A055548 2,12,80,2096,49792
%N A055548 Number of normal n X n (-1,1)-matrices.
%C A055548 Obviously a(n)<=2^(n^2)=A002416(n) - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Mar 14 2006
%D A055548 W. H. Press et al., Numerical Recipes, Cambridge, 1986; Chapter 11.
%H A055548 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               NormalMatrix.html">Link to a section of The World of Mathematics.</
               a>
%o A055548 (PARI) NormaQ(a,n) = { local(aT) ; aT=mattranspose(a) ; if( a*aT == aT*a,
               1,0) ; } combMat(no,n) = { local(a,noshif) ; a = matrix(n,n) ; noshif=no 
               ; for(co=1,n, for(ro=1,n, if( (noshif %2)== 1,a[ro,co] = 1, a[ro,
               co] = -1) ; noshif = floor(noshif/2) ; ) ) ; return(a) ; } { for 
               (n = 1, 10, count = 0; a = matrix(n,n) ; for( no=0,2^(n^2)-1, a = 
               combMat(no,n) ; count += NormaQ(a,n) ; if(no%1000==0,print(n," ",
               (no/2^(n^2)+0.)," ",count)) ; ) ; print(count) ; ) } - R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), Mar 14 2006
%Y A055548 Cf. A055547, A055549.
%Y A055548 Sequence in context: A063481 A052822 A058872 this_sequence A092850 A052864 
               A130464
%Y A055548 Adjacent sequences: A055545 A055546 A055547 this_sequence A055549 A055550 
               A055551
%K A055548 nonn,more
%O A055548 0,1
%A A055548 Eric Weisstein (eric(AT)weisstein.com)
%E A055548 a(5) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 14 2006

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