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A236680 Dimension of the space of spinors in n-dimensional real space. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 11 16:03 EST 2019. Contains 329019 sequences. (Running on oeis4.)