A089036 Number of n X n matrices over GF(3) with characteristic polynomial x^n - 1.

1, 12, 729, 758160, 2972290464, 354396766517640, 92079975413927255040, 939180873931369976460153600, 22528399544939174411840147874772641, 11276516942788127325350557035641264267894784, 25780902234356363794160964471948503247074139517747200

Offset: 1

Author

Yuval Dekel (dekelyuval(AT)hotmail.com) and W. Edwin Clark, Nov 29 2003

Keywords

• nonn

Links

• I. Reiner, On the number of matrices with given characteristic polynomial, Illinois J. Math. 5 1961 324-329.

Crossrefs

Cf. A088654, A089035, A089037.

Programs

PARI

\\ see Reiner reference.
F(u,r)={prod(i=1, r, (1-u^(-i)))}
a(n, q=3)={my(D=ffgen(q)); my(f=factor(D^0*(x^n-1))); q^(n^2-n)*F(q,n)/prod(i=1, #f~, F(q^poldegree(f[i,1]), f[i,2]))} \\ Andrew Howroyd, Jul 08 2018

Extensions

Offset corrected and a(9)-a(11) from Andrew Howroyd, Jul 08 2018