A226236 Number of semisimple invertible n X n matrices over GF(2).

1, 3, 105, 11025, 5439105, 11193473025, 89273960290305, 2926331900465537025, 380704455834655419367425, 200503685263248842050957082625, 418936006416927720918846481798529025, 3516831926000321799217446305276779638554625

Offset: 1

Author

Victor S. Miller, Jun 04 2013

Keywords

• nonn
• nice

Comments

Fulman shows that the ratio a(n)/A002884(n) converges to Product_{r>=1, r == 0,2,3 mod 5} (1-2^(-(r-1)))/(1-2^(-r)).

Examples

			a(2) = 3, the matrices are [[1,0],[0,1]], [[0,1],[1,1]], [[1,1],[1,0]].
		

Links

• Jason Fulman, Cycle Indices for the Finite Classical Groups, J. Group Thy., v. 2, 1999, 251-289.

Crossrefs

Cf. A225371 (every semisimple matrix over GF(2) is a square of another matrix).