A055548 Number of normal n X n (-1,1)-matrices.

2, 12, 80, 2096, 49792, 3449088, 357236224, 84783217408

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• more
• hard

Comments

Obviously a(n) <= 2^(n^2) = A002416(n) - R. J. Mathar, Mar 14 2006

References

• W. H. Press et al., Numerical Recipes, Cambridge, 1986; Chapter 11.

Links

• Georg Muntingh, Sage code for computing higher order entries
• Eric Weisstein's World of Mathematics, Normal matrix.

Crossrefs

Cf. A055547, A055549.

Programs

PARI

NormaQ(a,n) = { my(aT) ; aT=mattranspose(a) ; return( a*aT == aT*a ); }
combMat(no,n) = { my(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, Mar 14 2006

Extensions

a(5) from R. J. Mathar, Mar 14 2006

a(6)-a(7) from Georg Muntingh, Jan 31 2014

Offset corrected and a(8) from Bert Dobbelaere, Sep 21 2020