A089035 Number of n X n matrices over GF(2) with characteristic polynomial x^n - 1.

1, 4, 56, 4096, 666624, 1194590208, 3343877406720, 72057594037927936, 3701652434038082764800, 1021880992906173430024372224, 750836199529096452135514747699200, 7415506491123333639280491668337906941952, 52777360037873674206622083843242895013104844800

Offset: 1

Author

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

Keywords

• nonn

Links

• I. Reiner, On the number of matrices with given characteristic polynomial, Illinois J. Math. 5 1961 324-329.

Crossrefs

Cf. A088654, A089036, A089037, A335804.

Programs

PARI

\\ see Reiner reference.
F(u,r)={prod(i=1, r, (1-u^(-i)))}
a(n, q=2)={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

Extensions

Offset corrected and a(11)-a(13) from Andrew Howroyd, Jul 08 2018