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A055548 Number of normal n X n (-1,1)-matrices. +0
3
2, 12, 80, 2096, 49792 (list; graph; listen)
OFFSET

0,1

COMMENT

Obviously a(n)<=2^(n^2)=A002416(n) - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 14 2006

REFERENCES

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

LINKS

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

PROGRAM

(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

CROSSREFS

Cf. A055547, A055549.

Sequence in context: A063481 A052822 A058872 this_sequence A092850 A052864 A130464

Adjacent sequences: A055545 A055546 A055547 this_sequence A055549 A055550 A055551

KEYWORD

nonn,more

AUTHOR

Eric Weisstein (eric(AT)weisstein.com)

EXTENSIONS

a(5) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 14 2006

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Last modified September 6 16:04 EDT 2008. Contains 143483 sequences.


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