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
Keywords
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
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.