cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A236680 Dimension of the space of spinors in n-dimensional real space.

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%I A236680 #23 May 05 2019 10:57:01
%S A236680 1,2,4,4,4,4,8,8,16,32,64,64,64,64,128,128,256,512,1024,1024,1024,
%T A236680 1024,2048,2048,4096,8192,16384,16384,16384,16384,32768,32768,65536,
%U A236680 131072,262144,262144,262144,262144,524288,524288,1048576,2097152,4194304
%N A236680 Dimension of the space of spinors in n-dimensional real space.
%C A236680 a(n) = n only for n = 1, 2, 4, 8. These correspond to the four normed division algebras: the real numbers, the complex numbers, the quaternions, and the octonions.
%C A236680 All terms are powers of 2: a(n) = 2^A236916(n-1).
%H A236680 John Baez, <a href="http://www.youtube.com/watch?v=Tw8w4YPp4zM">John Baez on the number 8</a>, 2008 Rankin Lecture (see frame at 38 minutes and 5 seconds).
%H A236680 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,0,4,-8,8).
%F A236680 a(n) = 16*a(n-8) = 2*a(n-1) - 2*a(n-2) + 4*a(n-4) - 8*a(n-5) + 8*a(n-6).
%F A236680 G.f.: x*(1+2*x^2+4*x^5)/((1-2*x^2)*(1+2*x^2)*(1-2*x+2*x^2)). - _Colin Barker_, Jan 30 2014
%t A236680 LinearRecurrence[{2,-2,0,4,-8,8},{1,2,4,4,4,4},50] (* _Harvey P. Dale_, May 05 2019 *)
%o A236680 (PARI) Vec(x*(1+2*x^2+4*x^5)/((1-2*x^2)*(1+2*x^2)*(1-2*x+2*x^2)) + O(x^100)) \\ _Colin Barker_, Jan 30 2014
%Y A236680 Cf. A236916.
%Y A236680 Closely related to A034583 and A034584.
%K A236680 nonn,easy
%O A236680 1,2
%A A236680 _Charles R Greathouse IV_ and _William J. Keith_, Jan 29 2014