login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A089037 Number of n X n matrices over GF(5) with characteristic polynomial x^n - 1. 3
1, 30, 15500, 453375000, 95367431640625, 1200572419921875000000, 216114100769531250000000000000, 2795257557110966548919677734375000000000, 209657627533594448152542114257812500000000000000000, 1062251098375118429310154377631647548696491867303848266601562500 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 13 16:22 EDT 2020. Contains 335688 sequences. (Running on oeis4.)