A195679 Order of n-th homotopy group of the topological group O(oo), with -1 if the homotopy group is Z.

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

Colin Barker, Table of n, a(n) for n = 0..1000

John C. Baez, The Octonions, Bull. Amer. Math. Soc., 39 (2002), 145-205.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 1).

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

Adjacent sequences: A195676 A195677 A195678 * A195680 A195681 A195682

Keyword

sign,easy

Author

N. J. A. Sloane, Sep 22 2011

Extensions

Corrected by Harry Richman, Aug 27 2019

Status

approved