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A266462 The number of conjugacy classes of invertible n X n matrices over GF(2) which are squares of other such matrices. 4
1, 1, 2, 5, 10, 20, 41, 82, 166, 334, 667, 1336, 2682, 5360, 10724, 21467, 42936, 85876, 171786, 343574, 687184, 1374427, 2748852, 5497766, 10995706, 21991402, 43982908, 87966150, 175932383, 351864964, 703730584, 1407461288, 2814923196, 5629847656, 11259695532 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
It follows from the form of the generating function that a(n) is asymptotic to alpha*2^n where alpha = Product_{n>=1} (1-(1/16)^n)(1-2(1/2)^n)/ ((1-2(1/16)^n)(1-(1/4)^n))).
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 0..60 [Based on the table in Miller (2016)]
Victor S. Miller, Counting Matrices that are Squares, arXiv:1606.09299 [math.GR], 2016.
FORMULA
G.f.: Product_{n>=1} (1-2*x^(2*n))*(1-x^(2*n))/((1-2*x^n)*(1-2*x^(4*n))(1+x^(2*n-1))).
MATHEMATICA
terms = 35; CoefficientList[Product[(1-2x^(2n))(1-x^(2n))/((1-2x^n) (1-2x^(4n))(1+x^(2n-1))), {n, 1, terms}] + O[x]^terms, x] (* Jean-François Alcover, Aug 06 2018 *)
CROSSREFS
Cf. A006950.
Sequence in context: A049938 A002460 A266613 * A293319 A267589 A006836
KEYWORD
nonn
AUTHOR
Victor S. Miller, Dec 29 2015
EXTENSIONS
More terms from Alois P. Heinz, Dec 29 2015
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)