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A055548 Number of normal n X n (-1,1)-matrices. 3
2, 12, 80, 2096, 49792, 3449088, 357236224, 84783217408 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
Eric Weisstein's World of Mathematics, Normal matrix.
PROG
(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
CROSSREFS
Sequence in context: A292933 A058872 A340103 * A092850 A199420 A235348
KEYWORD
nonn,more,hard
AUTHOR
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
STATUS
approved

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Last modified February 21 07:54 EST 2024. Contains 370219 sequences. (Running on oeis4.)