A088853 Number of n X n matrices over GF(5) with characteristic polynomial x^(n-1) * (x-1).

1, 30, 19375, 304687500, 119171142578125, 1164078712463378906250, 284213456325232982635498046875, 1734719035084708593785762786865234375000, 264697660491697295270796530530788004398345947265625, 1009741855285318541798553204635879865236347541213035583496093750

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, A088852.

Programs

Mathematica

a[n_] := (5/4)*(5^(n^2-n) - 5^(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 = 5.

Extensions

More terms from Joerg Arndt, Oct 04 2013