A089036 Number of n X n matrices over GF(3) with characteristic polynomial x^n - 1.

1, 12, 729, 758160, 2972290464, 354396766517640, 92079975413927255040, 939180873931369976460153600, 22528399544939174411840147874772641, 11276516942788127325350557035641264267894784, 25780902234356363794160964471948503247074139517747200

Offset

1,2

Links

Table of n, a(n) for n=1..11.

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=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

Cf. A088654, A089035, A089037.

Sequence in context: A202792 A341560 A317337 * A273033 A276636 A284769

Adjacent sequences: A089033 A089034 A089035 * A089037 A089038 A089039

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