A089037 Number of n X n matrices over GF(5) with characteristic polynomial x^n - 1.

1, 30, 15500, 453375000, 95367431640625, 1200572419921875000000, 216114100769531250000000000000, 2795257557110966548919677734375000000000, 209657627533594448152542114257812500000000000000000, 1062251098375118429310154377631647548696491867303848266601562500

Offset

1,2

Links

Table of n, a(n) for n=1..10.

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

Prog

(PARI) \\ see Reiner reference.
F(u, r)={prod(i=1, r, (1-u^(-i)))}
a(n, q=5)={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

Crossrefs

Cf. A088654, A089035, A089036.

Sequence in context: A137749 A007741 A176378 * A116076 A230473 A088853

Adjacent sequences: A089034 A089035 A089036 * A089038 A089039 A089040

Keyword

nonn

Author

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

Extensions

Offset corrected and a(8)-a(10) from Andrew Howroyd, Jul 08 2018

Status

approved