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A226236 Number of semisimple invertible n X n matrices over GF(2). 0
1, 3, 105, 11025, 5439105, 11193473025, 89273960290305, 2926331900465537025, 380704455834655419367425, 200503685263248842050957082625, 418936006416927720918846481798529025, 3516831926000321799217446305276779638554625 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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)).

LINKS

Table of n, a(n) for n=1..12.

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

EXAMPLE

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

CROSSREFS

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

Sequence in context: A075528 A271049 A101485 * A074072 A226074 A037115

Adjacent sequences:  A226233 A226234 A226235 * A226237 A226238 A226239

KEYWORD

nonn,nice

AUTHOR

Victor S. Miller, Jun 04 2013

STATUS

approved

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Last modified December 14 19:52 EST 2018. Contains 318116 sequences. (Running on oeis4.)