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Search: id:A118127
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| A118127 |
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Number of quasigroups of order <= n. |
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+0
1
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| 1, 2, 3, 8, 43, 1454, 1131985, 12199587820, 2697830531268481, 15224736759268778589978, 2750892227033887206264514123491
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A quasigroup is a groupoid G such that for all a and b in G, there exist unique c and d in G such that ac = b, and da = b. Hence a quasigroup is not required to have an identity element, nor be associative. Equivalently, one can state that quasigroups are precisely groupoids whose multiplication tables are Latin squares (possibly empty).
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LINKS
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Index entries for sequences related to quasigroups.
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FORMULA
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a(n) = SUM[i=0..n] A057991(i).
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EXAMPLE
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a(10) = 2750892227033887206264514123491 = 1 + 1 + 1 + 5 + 35 + 1411 + 1130531 + 12198455835 + 2697818331680661 + 15224734061438247321497 + 2750892211809150446995735533513.
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CROSSREFS
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Cf. A002860, A057991-A057994, A057771, A057996, A118641.
Sequence in context: A127005 A042553 A042139 this_sequence A100644 A013208 A094370
Adjacent sequences: A118124 A118125 A118126 this_sequence A118128 A118129 A118130
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), May 12 2006
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