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A055548 Number of normal n X n (-1,1)-matrices. 3
2, 12, 80, 2096, 49792, 3449088, 357236224 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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

Table of n, a(n) for n=0..6.

Eric Weisstein's World of Mathematics, Normal matrix.

Georg Muntingh, Sage code for computing higher order entries

PROG

(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, Mar 14 2006

CROSSREFS

Cf. A055547, A055549.

Sequence in context: A246018 A292933 A058872 * A092850 A199420 A235348

Adjacent sequences:  A055545 A055546 A055547 * A055549 A055550 A055551

KEYWORD

nonn,more,hard

AUTHOR

Eric W. Weisstein

EXTENSIONS

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

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

STATUS

approved

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Last modified January 22 11:56 EST 2019. Contains 319363 sequences. (Running on oeis4.)