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A049332 Number of conjugacy classes in Clifford group CL(n). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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

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)). - Colin Barker, Apr 18 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-Fran├žois Alcover, Feb 11 2014 *)

LinearRecurrence[{2, 1, -2}, {2, 4, 5}, 40] (* Harvey P. Dale, Nov 29 2014 *)

PROG

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)

(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

Sequence in context: A253198 A138856 A018401 * A096570 A046430 A133040

Adjacent sequences:  A049329 A049330 A049331 * A049333 A049334 A049335

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 22 05:36 EST 2017. Contains 295076 sequences.