[seqfan] Re: Number of nXn (0,1)-matrices A with A^2=J?

Richard J. Mathar mathar at mpia-hd.mpg.de
Sat Mar 11 21:30:24 CET 2017

Related to http://list.seqfan.eu/pipermail/seqfan/2017-March/017328.html :

At least we can count the number of r-circulant nXn (0,1)-matrices with 
n=c^2, with c 1's in each row and each column (as required by Ryser)
that satisfy A^2=J_1. Short table of n and the count:
# 1 1
# 4 4
# 9 54
# 16 768
# 25 12500
# 36 93312

This starts like A071248 and A055774 and then disgresses.
That sort of computation needs about half an hour if one just
feeds all binary vectors with n elements and c 1's into the first row,
loops over all r from 0 to n-1, computes the squares, checks A^2=J,
and uses a hash-table (which is just the binary string of all 0's and 1's
converted to a big number) to avoid overcounts of the matches.


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