A088852 Number of n X n matrices over GF(4) with characteristic polynomial x^(n-1) * (x-1).

1, 20, 5376, 22282240, 1464583847936, 1536853372840181760, 25788843362951132511993856, 6922956840496417818923870380359680, 29734213503918523875893136571995338085236736, 2043325439152335369940571764620635289780959288334745600

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, A088671, A088853.

Programs

Mathematica

a[n_] := (4/3)*(4^(n^2-n) - 4^(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 = 4.

Extensions

More terms from Joerg Arndt, Oct 04 2013