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A226172
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The number of faithful connected quandles of order n.
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0
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1, 0, 1, 1, 3, 2, 5, 2, 8, 1, 9, 8, 11, 0, 7, 9, 15, 12, 17, 9, 9, 0, 21, 27, 34, 0, 62, 13, 27, 20, 29, 8, 11, 0, 15
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OFFSET
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1,5
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COMMENTS
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Let Q be a quandle with product *. Let R_a: x ->x*a for a,x in Q. By definition R_a is an automorphism of the quandle Q. If the mapping a->R_a is an injection then the quandle is said to be faithful. A quandle is faithful precisely when the columns of the Cayley table of the quandle are distinct.
This sequence was computed using Leandro Vendramin's list of all connected quandles of order at most 35.
Warning: Vendramin's quandles are assumed to be left distributive and hence one must reverse the order of the product to get the (right distributive) quandles used by knot theorists.
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LINKS
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CROSSREFS
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Cf. A181771 (gives the number of connected quandles of order n).
See also Index to OEIS under quandles.
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KEYWORD
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nonn,more,hard
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AUTHOR
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STATUS
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approved
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