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

1,2

Links

Table of n, a(n) for n=1..13.

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

Prog

(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

Crossrefs

Cf. A088654, A089036, A089037.

Sequence in context: A186252 A158262 A300513 * A327145 A089516 A361217

Adjacent sequences: A089032 A089033 A089034 * A089036 A089037 A089038

Keyword

nonn

Author

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

Extensions

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

Status

approved