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%I #55 Jan 28 2021 20:58:09
%S 1,2,10,260,31096,13711952,28275659056,224402782202048,
%T 7293836994286696576,952002419516769475035392,
%U 497678654312172407869125822976,1044660329769242614113093804053562368,8745525723307044762290950664928498588583936
%N a(n) = number of squares in M(n,2), the ring of n X n matrices over GF(2).
%C a(0)-a(4) computed by _W. Edwin Clark_, May 07 2013.
%C 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
%H Victor S. Miller, <a href="/A225371/b225371.txt">Table of n, a(n) for n = 0..30</a>
%H Victor S. Miller, <a href="http://arxiv.org/abs/1606.09299">Counting Matrices that are Squares</a>, arXiv:1606.09299 [math.GR], 2016.
%H Giovanni Resta, <a href="/A225371/a225371.c.txt">C program for a(k), with k <= 6.</a>
%H <a href="/index/Mat#binmat">Index entries for matrices, binary, which are squares</a>
%o (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
%o (PARI) ZM(k)=matrix(n,n,i,j,bittest(k,(i-1)*n+j-1))*Mod(1,2)
%o MZ(M)=my(n=matsize(M)[1]);sum(i=1,n,sum(j=1,n,M[i,j]<<((i-1)*n+j-1)))
%o a(n)=#vecsort(vector(2^n^2,i,MZ(lift(ZM(i,n)^2))),,8) \\ _Charles R Greathouse IV_, May 07 2013
%Y Cf. A226321, A121231, A266462, A274313.
%K nonn,hard
%O 0,2
%A _N. J. A. Sloane_, May 07 2013
%E a(5)-a(6) from _Giovanni Resta_, May 08 2013
%E a(7)-a(30) from _Victor S. Miller_, May 24 2013
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