A034583 Dimension of an irreducible R-module for Clifford algebra Cl_n.

1, 2, 4, 4, 8, 8, 8, 8, 16, 32, 64, 64, 128, 128, 128, 128, 256, 512, 1024, 1024, 2048, 2048, 2048, 2048, 4096, 8192, 16384, 16384, 32768, 32768, 32768, 32768, 65536, 131072, 262144, 262144, 524288, 524288, 524288, 524288, 1048576, 2097152, 4194304, 4194304, 8388608, 8388608, 8388608, 8388608, 16777216, 33554432, 67108864, 67108864, 134217728

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• H. Blaine Lawson, Jr. and M.-L. Michelsohn, Spin Geometry, Princeton, p. 33.
• Pertti Lounesto, Clifford Algebras and Spinors, Cambridge, 1997, p. 226.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• M. M. Balbino, I. P. de Freitas, R. G. Rana, and F. Toppan, Inequivalent Z_2^n-graded brackets, n-bit parastatistics and statistical transmutations of supersymmetric quantum mechanics, arXiv:2309.00965 [hep-th], 2023. See p. 19.
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,16).

Crossrefs

Cf. A034584, A034585, A034586.

Programs

PARI

Vec(-(8*x^7+8*x^6+8*x^5+8*x^4+4*x^3+4*x^2+2*x+1) / ((2*x^2-2*x+1)*(2*x^2-1)*(2*x^2+1)*(2*x^2+2*x+1)) + O(x^100)) \\ Colin Barker, Mar 27 2015

Formula

a(n) = 2^A034584(n). a(n+8) = 16*a(n).

G.f.: -(8*x^7+8*x^6+8*x^5+8*x^4+4*x^3+4*x^2+2*x+1) / ((2*x^2-2*x+1)*(2*x^2-1)*(2*x^2+1)*(2*x^2+2*x+1)). - Colin Barker, Mar 27 2015