A335804 Number of n X n matrices over GF(2) with minimal polynomial x^n - 1.

1, 3, 56, 2520, 666624, 839946240, 3343877406720, 41781748196966400, 3701652434038082764800, 763416952708225267547504640, 750836199529096452135514747699200

Offset

1,2

Comments

a(n) is the size of the conjugacy class in GL(n,GF(2)) corresponding to the companion matrix of x^n - 1. It can be given by the number of n X n invertible matrices over GF(2) divided by the number of n X n circulant invertible matrices over GF(2) (i.e., the centralizer of the companion matrix of x^n - 1).

Links

Table of n, a(n) for n=1..11.

Formula

a(n) = A002884(n) / A003473(n). If n is an odd prime, then a(n) = A089035(n).

Crossrefs

Cf. A002884, A003473, A027362, A089035.

Sequence in context: A241136 A202029 A287396 * A070731 A132489 A350336

Adjacent sequences: A335801 A335802 A335803 * A335805 A335806 A335807

Keyword

nonn

Author

Christof Beierle, Jun 24 2020

Status

approved