A060762 Number of conjugacy classes (the same as the number of irreducible representations) in the dihedral group with 2n elements.

2, 4, 3, 5, 4, 6, 5, 7, 6, 8, 7, 9, 8, 10, 9, 11, 10, 12, 11, 13, 12, 14, 13, 15, 14, 16, 15, 17, 16, 18, 17, 19, 18, 20, 19, 21, 20, 22, 21, 23, 22, 24, 23, 25, 24, 26, 25, 27, 26, 28, 27, 29, 28, 30, 29, 31, 30, 32, 31, 33, 32, 34, 33, 35, 34, 36, 35, 37, 36, 38, 37, 39, 38, 40

Offset

1,1

References

Jean-Pierre Serre, Linear Representations of Finite Groups, Springer-Verlag Graduate Texts in Mathematics 42.

Links

Harry J. Smith, Table of n, a(n) for n=1,...,1000

Index entries for linear recurrences with constant coefficients, signature (1, 1, -1).

Formula

For odd n: a(n) = (n+3)/2; for even n: a(n) = (n+6)/2.

a(1)=2,a(2)=4. For odd n:a(n)=(a(n-1)+a(n-2))/2; for even n: a(n)=(a(n-1)+a(n-2)+3)/2. [Vincenzo Librandi, Dec 20 2010]

a(n)=a(n-1)+a(n-2)-a(n-3). G.f.: x*(2+2*x-3*x^2)/((1-x)^2*(1+x)). [Colin Barker, Apr 19 2012]

Mathematica

a[1] = 2; a[2] = 4; a[n_] := a[n] = (a[n - 1] + a[n - 2] + If[ OddQ@ n, 0, 3])/2; Array[a, 74]
LinearRecurrence[{1, 1, -1}, {2, 4, 3}, 74] (* Robert G. Wilson v, Apr 19 2012 *)

Prog

(Magma) [ IsOdd(n) select (n+3)/2 else n/2+3 : n in [1..10] ]; // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
(PARI) { for (n=1, 1000, if (n%2, a=(n + 3)/2, a=(n + 6)/2); write("b060762.txt", n, " ", a); ) } \\ Harry J. Smith, Jul 11 2009

Crossrefs

Sequence in context: A283366 A048186 A352196 * A371924 A328793 A195782

Adjacent sequences: A060759 A060760 A060761 * A060763 A060764 A060765

Keyword

nonn,easy

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 23 2001

Extensions

More terms from Jonathan Vos Post, May 27 2007

Status

approved