A088671 Number of n X n matrices over GF(3) with characteristic polynomial x^(n-1) * (x-1).

1, 12, 1053, 787320, 5208653241, 308413053837252, 164053436379620039253, 784901799876425497055472240, 33790882475498615361517892887614321, 13091723638887447119952122094399781435115772, 45648533143796439623892471646730372987043769546194573

Offset: 1

Author

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

Keywords

• nonn

Links

• Irving Reiner, On the number of matrices with given characteristic polynomial, Illinois Journal of Mathematics, Vol. 5, No. 2 (1961), pp. 324-329.

Crossrefs

Cf. A088668, A088852, A088853.

Programs

Mathematica

a[n_] := (3/2)*(3^(n^2-n) - 3^(n^2-2*n)); Array[a, 10] (* Amiram Eldar, Jul 13 2025 *)

Formula

a(n) = (q/(q-1))*(q^(n^2-n)-q^(-2*n+n^2)) where q = 3.

Extensions

More terms from Joerg Arndt, Oct 04 2013