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

1, 2, 4, 4, 4, 4, 8, 8, 16, 32, 64, 64, 64, 64, 128, 128, 256, 512, 1024, 1024, 1024, 1024, 2048, 2048, 4096, 8192, 16384, 16384, 16384, 16384, 32768, 32768, 65536, 131072, 262144, 262144, 262144, 262144, 524288, 524288, 1048576, 2097152, 4194304

Offset: 1

Author

Charles R Greathouse IV and William J. Keith, Jan 29 2014

Keywords

• nonn
• easy

Comments

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.

All terms are powers of 2: a(n) = 2^A236916(n-1).

Links

• John Baez, John Baez on the number 8, 2008 Rankin Lecture (see frame at 38 minutes and 5 seconds).
• Index entries for linear recurrences with constant coefficients, signature (2,-2,0,4,-8,8).

Crossrefs

Cf. A236916.

Closely related to A034583 and A034584.

Programs

Mathematica

LinearRecurrence[{2,-2,0,4,-8,8},{1,2,4,4,4,4},50] (* Harvey P. Dale, May 05 2019 *)

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

Formula

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).

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