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

0,1

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).

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

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 *)

Prog

(Magma) [(3/2-(-1)^n/2+2^n): n in [0..40]]; // Vincenzo Librandi, Apr 27 2012
(PARI) a(n) = 3/2 - (-1)^n/2 + 2^n \\ Charles R Greathouse IV, Feb 10 2017

Crossrefs

Cf. A101622, A014551 (first differences)

Sequence in context: A138856 A333188 A018401 * A335206 A096570 A046430

Adjacent sequences: A049329 A049330 A049331 * A049333 A049334 A049335

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Status

approved