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%I #48 Mar 06 2024 15:45:18
%S 2,4,5,10,17,34,65,130,257,514,1025,2050,4097,8194,16385,32770,65537,
%T 131074,262145,524290,1048577,2097154,4194305,8388610,16777217,
%U 33554434,67108865,134217730,268435457,536870914,1073741825,2147483650
%N Number of conjugacy classes in Clifford group CL(n).
%C 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)
%D B. Simon, Representations of Finite and Compact Groups, Amer. Math. Soc., 1996, p. 69.
%H Vincenzo Librandi, <a href="/A049332/b049332.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2).
%F a(n+2) - A101622(n+1) = 4. - _Creighton Dement_, Mar 07 2005
%F From _Colin Barker_, Apr 18 2012: (Start)
%F a(n) = (3/2 - (-1)^n/2 + 2^n).
%F a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3).
%F G.f.: (2-5*x^2)/((1-x)*(1+x)*(1-2*x)). (End)
%F E.g.f.: cosh(x) + cosh(2*x) + 2*sinh(x) + sinh(2*x). - _Stefano Spezia_, May 27 2022
%F a(n) = 2*A000975(n+1) -5*A000975(n-1). - _R. J. Mathar_, Oct 12 2022
%p A049332 := proc(n) if n mod 2 = 0 then 2^n+1 else 2^n+2; fi; end;
%t CoefficientList[Series[(2-5*x^2)/((1-x)*(1+x)*(1-2*x)),{x,0,40}],x] (* _Vincenzo Librandi_, Apr 27 2012 *)
%t Table[2^n + Mod[n, 2] + 1, {n, 0, 31}] (* _Jean-François Alcover_, Feb 11 2014 *)
%t LinearRecurrence[{2,1,-2},{2,4,5},40] (* _Harvey P. Dale_, Nov 29 2014 *)
%o (Magma) [(3/2-(-1)^n/2+2^n): n in [0..40]]; // _Vincenzo Librandi_, Apr 27 2012
%o (PARI) a(n) = 3/2 - (-1)^n/2 + 2^n \\ _Charles R Greathouse IV_, Feb 10 2017
%Y Cf. A101622, A014551 (first differences)
%K nonn,nice,easy
%O 0,1
%A _N. J. A. Sloane_
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