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

Author

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

Keywords

• nonn
• easy

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).

Programs

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

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 *)

PARI

a(n) = { if (n%2, (n + 3)/2, (n + 6)/2) } \\ Harry J. Smith, Jul 11 2009

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

From Colin Barker, Apr 19 2012: (Start)

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)). (End)

Extensions

More terms from Jonathan Vos Post, May 27 2007