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Number of loops of order n that are not groups.
0

%I #30 Feb 02 2020 21:37:00

%S 0,0,0,0,0,5,107,23745,106228844,9365022303538,20890436195945769615,

%T 1478157455158044452849321015

%N Number of loops of order n that are not groups.

%C A loop is a quasigroup with an identity element. - _Muniru A Asiru_, Dec 13 2018

%H A. Hulpke, Petteri Kaski and Patric R. J. Östergård, <a href="http://dx.doi.org/10.1090/S0025-5718-2010-02420-2">The number of Latin squares of order 11</a>, Math. Comp. 80 (2011) 1197-1219.

%H Brendan D. McKay, A. Meynert and W. Myrvold, <a href="http://users.cecs.anu.edu.au/~bdm/papers/ls_final.pdf">Small Latin Squares, Quasigroups and Loops</a>, J. Combin. Designs 15 (2007), no. 2, 98-119.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Quasigroup">Quasigroup</a>

%H <a href="/index/Qua#quasigroups">Index entries for sequences related to quasigroups</a>

%F a(n) = A057771(n) - A000001(n).

%Y Cf. A057771, A000001.

%K nonn,more

%O 0,6

%A _Steve Szabo_, Sep 06 2018

%E a(7)-a(11) from _Muniru A Asiru_, Dec 07 2018

%E a(0) prepended by _Jianing Song_, Oct 26 2019