A088668 Number of n X n matrices over GF(2) with characteristic polynomial x^(n-1) * (x-1).

1, 6, 112, 7680, 2031616, 2113929216, 8727373545472, 143552238122434560, 9426286221665580875776, 2473462226931531291448836096, 2594880778667185584863751461404672, 10886377285478460999082179823696022077440, 182665403921164334152319068371262729095485587456

Offset: 1

Author

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

Keywords

• nonn
• easy

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. A088671, A088852, A088853.

Programs

Mathematica

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

PARI

a(n)=(2^n-1)<<(n^2-2*n+1) \\ Charles R Greathouse IV, Oct 04 2013

Formula

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

Extensions

More terms from Joerg Arndt, Oct 04 2013