

A060762


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


4



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
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OFFSET

1,1


REFERENCES

JeanPierre Serre, Linear Representations of Finite Groups, SpringerVerlag Graduate Texts in Mathematics 42.


LINKS



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(n1)+a(n2))/2; for even n: a(n)=(a(n1)+a(n2)+3)/2. [Vincenzo Librandi, Dec 20 2010]
a(n)=a(n1)+a(n2)a(n3). G.f.: x*(2+2*x3*x^2)/((1x)^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]


PROG

(Magma) [ IsOdd(n) select (n+3)/2 else n/2+3 : n in [1..10] ]; // Sergei Haller (sergei(AT)sergeihaller.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



KEYWORD

nonn,easy


AUTHOR

Ahmed Fares (ahmedfares(AT)mydeja.com), Apr 23 2001


EXTENSIONS



STATUS

approved



