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A274313 The number of conjugacy classes of n X n matrices over GF(2) which are squares of other such matrices. 3
1, 2, 4, 10, 22, 46, 96, 198, 406, 826, 1668, 3362, 6770, 13590, 27248, 54614, 109378, 218946, 438180, 876738, 1753998, 3508726, 7018368, 14038006, 28077846, 56157954, 112318900, 224642090, 449289666, 898586438, 1797182704, 3594378014, 7188772666, 14377567834, 28755164100, 57510365698, 115020782350, 230041628622, 460083340304, 920166792942 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1000 (terms 0..60 from N. J. A. Sloane)

Victor S. Miller, Counting Matrices that are Squares, arXiv:1606.09299 [math.GR], 2016.

Index entries for matrices, binary, which are squares

FORMULA

G.f.: Product_{n>=1} (1-2*z^(2*n))/((1-2*z^n)*(1-2*z^(4*n)). - Jean-François Alcover, Dec 12 2018, after Victor S. Miller.

MAPLE

seq(coeff(series(mul((1-2*x^(2*k))/((1-2*x^k)*(1-2*x^(4*k))), k=1..n), x, n+1), x, n), n = 0 .. 40); # Muniru A Asiru, Dec 13 2018

MATHEMATICA

terms = 40;

Product[(1-2z^(2n))/(1-2z^n)/(1-2z^(4n)), {n, 1, terms}] + O[z]^terms // CoefficientList[#, z]& (* Jean-François Alcover, Dec 12 2018 *)

PROG

(PARI) seq(n)=Vec(prod(i=1, n, (1-2*x^(2*i))/((1-2*x^i)*(1-2*x^(4*i)) + O(x*x^n)))) \\ Andrew Howroyd, Dec 12 2018

(MAGMA) m:=40; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (&*[(1-2*x^(2*k))/((1-2*x^k)*(1-2*x^(4*k))): k in [1..m/2]]))); // G. C. Greubel, Dec 16 2018

(Sage) m=40; s=(prod((1-2*x^(2*k))/((1-2*x^k)*(1-2*x^(4*k))) for k in (1..m/2))).series(x, m); s.coefficients(x, sparse=False) # G. C. Greubel, Dec 16 2018

CROSSREFS

Cf. A266462.

Sequence in context: A005306 A075898 A337654 * A291397 A091618 A181158

Adjacent sequences:  A274310 A274311 A274312 * A274314 A274315 A274316

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 25 2016

STATUS

approved

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Last modified January 20 08:54 EST 2022. Contains 350471 sequences. (Running on oeis4.)