

A225371


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


5



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

0,2


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


PROG

(PARI) a(n)=#vecsort(lift(vector(2^n^2, k, matrix(n, n, i, j, bittest(k, (i1)*n+j1))^2*Mod(1, 2))), , 8) \\ Charles R Greathouse IV, May 07 2013
(PARI) ZM(k)=matrix(n, n, i, j, bittest(k, (i1)*n+j1))*Mod(1, 2)
MZ(M)=my(n=matsize(M)[1]); sum(i=1, n, sum(j=1, n, M[i, j]<<((i1)*n+j1)))
a(n)=#vecsort(vector(2^n^2, i, MZ(lift(ZM(i, n)^2))), , 8) \\ Charles R Greathouse IV, May 07 2013


CROSSREFS

Cf. A226321, A121231, A266462, A274313.
Sequence in context: A289948 A282567 A308756 * A088310 A134473 A005154
Adjacent sequences: A225368 A225369 A225370 * A225372 A225373 A225374


KEYWORD

nonn,hard


AUTHOR

N. J. A. Sloane, 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


STATUS

approved



