A089599 G.f.: (1+x^5+x^7+x^8+x^10+x^15)/((1-x^2)(1-x^3)(1-x^4)(1-x^6)^2(1-x^9)).

1, 0, 1, 1, 2, 2, 5, 4, 8, 9, 13, 15, 23, 24, 35, 40, 52, 60, 79, 87, 112, 127, 155, 177, 216, 240, 290, 326, 382, 430, 503, 557, 648, 720, 822, 914, 1041, 1144, 1298, 1428, 1600, 1760, 1967, 2146, 2392, 2609, 2882, 3142, 3463, 3752, 4127, 4468, 4882, 5282, 5760, 6202

Offset: 0

Author

N. J. A. Sloane, Dec 31 2003

Keywords

• nonn

Comments

Poincaré series [or Poincare series] (or Molien series) for (P[x_0, x_1] ⊗ P[x_0, x_1] ⊗ P[x_0, x_1] )^(S_3).

References

• A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 200.

Links

• Ray Chandler, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 0, -2, 1, -1, 0, 2, -2, 1, 0, 0, 1, -2, 2, 0, -1, 1, -2, 0, 0, 1, 1, -1).

Crossrefs

Cf. A082146, A091434, A091726, A091769.

Programs

PARI

Vec((1+x^5+x^7+x^8+x^10+x^15)/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^6)^2*(1-x^9)) + O(x^100)) \\ Michel Marcus, Mar 19 2014

Formula

G.f.: (1-x+x^5-x^9+x^10)/((1-x)^2*(1-x^2)*(1-x^4)*(1-x^6)*(1-x^9)*(1+x+x^2)). See also the NAME. - Wolfdieter Lang, Mar 19 2014