A049332 Number of conjugacy classes in Clifford group CL(n).

2, 4, 5, 10, 17, 34, 65, 130, 257, 514, 1025, 2050, 4097, 8194, 16385, 32770, 65537, 131074, 262145, 524290, 1048577, 2097154, 4194305, 8388610, 16777217, 33554434, 67108865, 134217730, 268435457, 536870914, 1073741825, 2147483650

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

Comments

Floretion Algebra Multiplication Program, FAMP Code: 4tesforseq[ (- .25'i - .25i' - .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' - .25e)*( + .5'i + .5i' + .5'ii' + .5'jk' + .5'kj' + .5e ) ], 1vesforseq = (1,1,1,1,1,1,1). (Dement)

References

• B. Simon, Representations of Finite and Compact Groups, Amer. Math. Soc., 1996, p. 69.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

Crossrefs

Cf. A101622, A014551 (first differences)

Programs

Magma

[(3/2-(-1)^n/2+2^n): n in [0..40]]; // Vincenzo Librandi, Apr 27 2012

Maple

A049332 := proc(n) if n mod 2 = 0 then 2^n+1 else 2^n+2; fi; end;

Mathematica

CoefficientList[Series[(2-5*x^2)/((1-x)*(1+x)*(1-2*x)),{x,0,40}],x] (* Vincenzo Librandi, Apr 27 2012 *)
Table[2^n + Mod[n, 2] + 1, {n, 0, 31}] (* Jean-François Alcover, Feb 11 2014 *)
LinearRecurrence[{2,1,-2},{2,4,5},40] (* Harvey P. Dale, Nov 29 2014 *)

PARI

a(n) = 3/2 - (-1)^n/2 + 2^n \\ Charles R Greathouse IV, Feb 10 2017

Formula

a(n+2) - A101622(n+1) = 4. - Creighton Dement, Mar 07 2005

From Colin Barker, Apr 18 2012: (Start)

a(n) = (3/2 - (-1)^n/2 + 2^n).

a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3).

G.f.: (2-5*x^2)/((1-x)*(1+x)*(1-2*x)). (End)

E.g.f.: cosh(x) + cosh(2*x) + 2*sinh(x) + sinh(2*x). - Stefano Spezia, May 27 2022

a(n) = 2*A000975(n+1) -5*A000975(n-1). - R. J. Mathar, Oct 12 2022