A274313 The number of conjugacy classes of n X n matrices over GF(2) which are squares of other such matrices.

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

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: A360631 A337654 A369491 * A291397 A091618 A181158

Adjacent sequences: A274310 A274311 A274312 * A274314 A274315 A274316

Keyword

nonn

Author

N. J. A. Sloane, Jun 25 2016

Status

approved