A088654 Number of n X n matrices over GF(4) with characteristic polynomial x^n - 1.

1, 16, 6720, 16777216, 1148854468608, 2283836902459047936, 18326253047993428082688000, 5192296858534827628530496329220096, 37561472427665521549351504937293279395840000, 1720883444277066617294561853430153730874784623341076480

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. A089035, A089036, A089037.

Programs

PARI

\\ see Reiner reference.
F(u,r)={prod(i=1, r, (1-u^(-i)))}
a(n, q=4)={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(8)-a(10) from Andrew Howroyd, Jul 08 2018