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A034583 Dimension of an irreducible R-module for Clifford algebra Cl_n. 6


%S 1,2,4,4,8,8,8,8,16,32,64,64,128,128,128,128,256,512,1024,1024,2048,

%T 2048,2048,2048,4096,8192,16384,16384,32768,32768,32768,32768,65536,

%U 131072,262144,262144,524288,524288,524288,524288,1048576,2097152,4194304,4194304,8388608,8388608,8388608,8388608,16777216,33554432,67108864,67108864,134217728

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

%D H. Blaine Lawson, Jr. and M.-L. Michelsohn, Spin Geometry, Princeton, p. 33.

%D Pertti Lounesto, Clifford Algebras and Spinors, Cambridge, 1997, p. 226.

%H Colin Barker, <a href="/A034583/b034583.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,16).

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

%F 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

%o (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

%Y Cf. A034584, A034585, A034586.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

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Last modified August 9 22:07 EDT 2020. Contains 336326 sequences. (Running on oeis4.)