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A195679
Order of n-th homotopy group of the topological group O(oo), with -1 if the homotopy group is Z.
2
2, 2, 1, -1, 1, 1, 1, -1, 2, 2, 1, -1, 1, 1, 1, -1, 2, 2, 1, -1, 1, 1, 1, -1, 2, 2, 1, -1, 1, 1, 1, -1, 2, 2, 1, -1, 1, 1, 1, -1, 2, 2, 1, -1, 1, 1, 1, -1, 2, 2, 1, -1, 1, 1, 1, -1, 2, 2, 1, -1, 1, 1, 1, -1, 2, 2, 1, -1, 1, 1, 1, -1, 2, 2, 1, -1, 1, 1, 1, -1, 2, 2, 1, -1, 1, 1, 1, -1, 2, 2, 1, -1, 1, 1, 1, -1, 2, 2, 1, -1, 1, 1, 1, -1, 2, 2, 1, -1, 1, 1, 1, -1, 2, 2, 1, -1, 1, 1, 1, -1
OFFSET
0,1
COMMENTS
Computed by R. Bott in 1957. Periodic with period 8.
LINKS
John C. Baez, The Octonions, Bull. Amer. Math. Soc., 39 (2002), 145-205.
FORMULA
From Colin Barker, Aug 28 2019: (Start)
G.f.: (1 + x + x^2)*(2 - x^2 + 2*x^4 - x^5) / ((1 - x)*(1 + x)*(1 + x^2)*(1 + x^4)).
a(n) = a(n-8) for n>7.
(End)
MATHEMATICA
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1}, {2, 2, 1, -1, 1, 1, 1, -1}, 128] (* Ray Chandler, Aug 25 2015 *)
PROG
(PARI) Vec((1 + x + x^2)*(2 - x^2 + 2*x^4 - x^5) / ((1 - x)*(1 + x)*(1 + x^2)*(1 + x^4)) + O(x^100)) \\ Colin Barker, Aug 28 2019
CROSSREFS
Cf. A047530.
Sequence in context: A296978 A236000 A114139 * A029884 A309997 A118164
KEYWORD
sign,easy
AUTHOR
N. J. A. Sloane, Sep 22 2011
EXTENSIONS
Corrected by Harry Richman, Aug 27 2019
STATUS
approved