A266462 -id:A266462 - cp's OEIS frontend

A225371 a(n) = number of squares in M(n,2), the ring of n X n matrices over GF(2).

1, 2, 10, 260, 31096, 13711952, 28275659056, 224402782202048, 7293836994286696576, 952002419516769475035392, 497678654312172407869125822976, 1044660329769242614113093804053562368, 8745525723307044762290950664928498588583936

Offset: 0

N. J. A. Sloane, May 07 2013

a(0)-a(4) computed by W. Edwin Clark, May 07 2013.

A226321 is a similar sequence which counts the real {0,1} matrices which are the square of a {0,1} matrix. - Giovanni Resta, Jun 03 2013

Victor S. Miller, Table of n, a(n) for n = 0..30
Victor S. Miller, Counting Matrices that are Squares, arXiv:1606.09299 [math.GR], 2016.
Giovanni Resta, C program for a(k), with k <= 6.
Index entries for matrices, binary, which are squares

Cf. A226321, A121231, A266462, A274313.

a(n)=#vecsort(lift(vector(2^n^2,k,matrix(n,n,i,j,bittest(k,(i-1)*n+j-1))^2*Mod(1,2))),,8) \\ Charles R Greathouse IV, May 07 2013

ZM(k)=matrix(n,n,i,j,bittest(k,(i-1)*n+j-1))*Mod(1,2)
MZ(M)=my(n=matsize(M)[1]);sum(i=1,n,sum(j=1,n,M[i,j]<<((i-1)*n+j-1)))
a(n)=#vecsort(vector(2^n^2,i,MZ(lift(ZM(i,n)^2))),,8) \\ Charles R Greathouse IV, May 07 2013

a(5)-a(6) from Giovanni Resta, May 08 2013

a(7)-a(30) from Victor S. Miller, May 24 2013

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

N. J. A. Sloane, Jun 25 2016

nonn

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

Cf. A266462.

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

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

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 *)

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

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

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.

A274314 a(n) = number of squares in GL(n,2), the ring of invertible n X n matrices over GF(2).

Original entry on oeis.org

1, 1, 3, 126, 11340, 5940840, 12076523928, 95052257647200, 3153668941285723200, 406198470650573931200640, 215366179177149634500004545792, 447870507819487666185959047316144640, 3770394197251690930118967532374966498493440, 126205342254129164806148123600990735262978861434880, 16960349752279776751561660450391351891796348875427924676608

Offset: 0

N. J. A. Sloane, Jun 25 2016

nonn

Victor S. Miller, Counting Matrices that are Squares, arXiv:1606.09299 [math.GR], 2016.
Index entries for matrices, binary, which are squares

Cf. A266462, A274313, A225371.

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A225371 a(n) = number of squares in M(n,2), the ring of n X n matrices over GF(2).

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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.

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A274314 a(n) = number of squares in GL(n,2), the ring of invertible n X n matrices over GF(2).

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