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 A177886 The number of isomorphism classes of latin quandles of order n. 1
 1, 0, 1, 1, 3, 0, 5, 2, 8, 0, 9, 1, 11, 0, 5, 9, 15, 0, 17, 3, 7, 0, 21, 2, 34, 0, 62, 7, 27, 0, 29, 8, 11, 0, 15 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS A quandle is latin if its multiplication table is a latin square.  A latin quandle may be described as a left (or right) distributive quasigroup. Sherman Stein (see reference below) proved that a left distributive quasigroup of order n exists if and only if n is not of the form 4k + 2. REFERENCES S. K. Stein, On the Foundations of Quasigroups, Transactions of American Mathematical Society, 85 (1957),228-256. LINKS G. Ehrman, A. Gurpinar, M. Thibault, D. Yetter, Some Sharp Ideas on Quandle Construction S. Nelson, A polynomial invariant of finite quandles S. K. Stein, On the foundations of quasigroups Leandro Vendramin, On the classification of quandles of low order, arXiv:1105.5341v1 [math.GT]. Leandro Vendramin and Matías Graña, Rig, a GAP package for racks and quandles. EXAMPLE a(2) = 0 since the only quandle of order 2 has multiplication table with rows [1,1] and [2,2]. PROG GAP with the Rig Package LoadPackage("rig"); a:=[1, 0];; Print(1, ", "); Print(0, ", "); for n in [3..35] do a[n]:=0; for i in [1..NrSmallQuandles(n)] do if IsLatin(SmallQuandle(n, i)) then   a[n]:=a[n]+1; fi; od; Print(a[n], ", "); od; CROSSREFS Cf. A181769, A176077, A181771 Sequence in context: A175297 A165754 A193067 * A011293 A181884 A201565 Adjacent sequences:  A177883 A177884 A177885 * A177887 A177888 A177889 KEYWORD nonn,more AUTHOR W. Edwin Clark, Dec 14 2010 EXTENSIONS Added fact due to S. K. Stein that a(4k+2) = 0 and a reference to Stein's paper. a(11)-a(35) from W. Edwin Clark, Nov 26 2011 Links to the rig Gap package by W. Edwin Clark, Nov 26 2011 GAP program to compute the sequence up to n = 35 by W. Edwin Clark, Nov 26 2011 STATUS approved

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