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A089036
Number of n X n matrices over GF(3) with characteristic polynomial x^n - 1.
3
1, 12, 729, 758160, 2972290464, 354396766517640, 92079975413927255040, 939180873931369976460153600, 22528399544939174411840147874772641, 11276516942788127325350557035641264267894784, 25780902234356363794160964471948503247074139517747200
OFFSET
1,2
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Yuval Dekel (dekelyuval(AT)hotmail.com) and W. Edwin Clark, Nov 29 2003
EXTENSIONS
Offset corrected and a(9)-a(11) from Andrew Howroyd, Jul 08 2018
STATUS
approved