cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

N. J. A. Sloane, Jun 25 2016

Keywords

Crossrefs

Cf. A266462.

Programs

  • Magma
    m:=40; R:=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
    
  • 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 *)
  • 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
    
  • 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

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.