cp's OEIS Frontend

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

%I A195679 #23 Sep 08 2019 11:43:26
%S A195679 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,
%T A195679 -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,
%U A195679 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
%N A195679 Order of n-th homotopy group of the topological group O(oo), with -1 if the homotopy group is Z.
%C A195679 Computed by R. Bott in 1957. Periodic with period 8.
%H A195679 Colin Barker, <a href="/A195679/b195679.txt">Table of n, a(n) for n = 0..1000</a>
%H A195679 John C. Baez, <a href="http://math.ucr.edu/home/baez/octonions/">The Octonions</a>, Bull. Amer. Math. Soc., 39 (2002), 145-205.
%H A195679 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 1).
%F A195679 From _Colin Barker_, Aug 28 2019: (Start)
%F A195679 G.f.: (1 + x + x^2)*(2 - x^2 + 2*x^4 - x^5) / ((1 - x)*(1 + x)*(1 + x^2)*(1 + x^4)).
%F A195679 a(n) = a(n-8) for n>7.
%F A195679 (End)
%t A195679 LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1},{2, 2, 1, -1, 1, 1, 1, -1},128] (* _Ray Chandler_, Aug 25 2015 *)
%o A195679 (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
%Y A195679 Cf. A047530.
%K A195679 sign,easy
%O A195679 0,1
%A A195679 _N. J. A. Sloane_, Sep 22 2011
%E A195679 Corrected by _Harry Richman_, Aug 27 2019