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A132126
Number of nonassociative subloops of order 8n of the Cayley octonions (up to isomorphism).
1
0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
1,6
COMMENTS
Every nonassociative subloop of the octonions has order a multiple of 8.
LINKS
P. Boddington and D. Rumynin, On Curtis' theorem about finite octonionic loops, Proc. Amer. Math. Soc. 135 (2007), 1651-1657.
FORMULA
a(1) = 0, a(6) = 2, a(12) = 2, a(30) = 3, otherwise a(n) = 1.
MATHEMATICA
ReplacePart[PadRight[{0}, 120, 1], {6->2, 12->2, 30->3}] (* Harvey P. Dale, Dec 18 2018 *)
PROG
(PARI) A132126(n) = if(1==n, 0, if((6==n)||(12==n), 2, if(30==n, 3, 1))); \\ Antti Karttunen, Sep 27 2018
CROSSREFS
Cf. A090750.
Sequence in context: A329801 A053255 A085856 * A324882 A345047 A031264
KEYWORD
easy,nonn
AUTHOR
Paul Boddington, Oct 31 2007
STATUS
approved