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

1,2

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

Table of n, a(n) for n=1..43.

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).

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A236916.

Closely related to A034583 and A034584.

Sequence in context: A220495 A194441 A220521 * A162798 A088650 A097154

Adjacent sequences: A236677 A236678 A236679 * A236681 A236682 A236683

Keyword

nonn,easy

Author

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

Status

approved