A082642 Expansion of Molien series for 5-dimensional representation of dihedral group of order 10.

1, 0, 1, 2, 3, 4, 5, 6, 9, 10, 13, 14, 17, 20, 23, 26, 29, 32, 37, 40, 45, 48, 53, 58, 63, 68, 73, 78, 85, 90, 97, 102, 109, 116, 123, 130, 137, 144, 153, 160, 169, 176, 185, 194, 203, 212, 221, 230, 241, 250, 261, 270, 281, 292, 303, 314, 325, 336, 349, 360, 373, 384, 397, 410

Offset

0,4

References

M. D. Neusel and L. Smith, Invariant Theory of Finite Groups, Amer. Math. Soc., 2002; see p. 149.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,1,-1,-1,1).

Formula

G.f.: (1+x^2+x^3+2*x^4+2*x^5+2*x^6+x^7+x^8+x^10)/((1-x^3)*(1-x^4)*(1-x^5)).

G.f.: -(x^6-x^5+2*x^3-x+1) / ((x-1)^3*(x+1)*(x^4+x^3+x^2+x+1)). - Colin Barker, Apr 02 2015

Mathematica

CoefficientList[Series[(1 + x^2 + x^3 + 2 x^4 + 2 x^5 + 2 x^6 + x^7 + x^8 +x^10) / ((1 - x^3) (1 - x^4) (1 - x^5)), {x, 0, 70}], x] (* Vincenzo Librandi, Aug 15 2013 *)

Prog

(PARI) Vec(-(x^6-x^5+2*x^3-x+1)/((x-1)^3*(x+1)*(x^4+x^3+x^2+x+1)) + O(x^100)) \\ Colin Barker, Apr 02 2015

Crossrefs

Sequence in context: A134950 A018321 A178971 * A217348 A319450 A153013

Adjacent sequences: A082639 A082640 A082641 * A082643 A082644 A082645

Keyword

nonn,easy

Author

N. J. A. Sloane, May 15 2003

Status

approved