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3^a(n) is the order of the free commutative Moufang loop of exponent 3 on n generators.
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%I #17 Sep 28 2021 18:41:33

%S 4,12,49,220,1014

%N 3^a(n) is the order of the free commutative Moufang loop of exponent 3 on n generators.

%D Yu. I. Manin, Cubic forms, Amsterdam: North-Holland, 1979.

%D Yu. I. Manin, Cubic Forms, Second edition, North-Holland Publishing Co., Amsterdam, 1986, page 312. MR0833513 (87d:11037)

%H Alexander N. Grishkov and Ivan P. Shestakov, <a href="http://arxiv.org/abs/0811.3787">Commutative Moufang loops and alternative algebras</a>, arXiv:0811.3787 [math.RA], 2008.

%H Marina Rasskazova, Alexandre Grichkov and Henrique Guzzo, <a href="https://impa.br/wp-content/uploads/2019/07/32CBM-P_MarinaRasskazova.pdf">Commutative Moufang loops and cubic hypersurface</a>, 32o Colóquio Brasileiro de Matemática, IMPA, 2019.

%H Jonathan D. H. Smith, <a href="http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN002098156">Commutative Moufang loops and Bessel functions</a>, Invent. Math. 67 (1982), no. 1, 173-187.

%Y Cf. A000373, A090750, A118641.

%K nonn,more

%O 3,1

%A _Jonathan Vos Post_, Nov 25 2008

%E Definition changed and a(7) changed by _Andrey Zabolotskiy_, Sep 28 2021