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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
OFFSET
1,2
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
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