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

Author

N. J. A. Sloane, May 07 2013

Keywords

• nonn
• hard

Comments

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

Links

• 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

Crossrefs

Cf. A226321, A121231, A266462, A274313.

Programs

PARI

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

PARI

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

Extensions

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

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