OFFSET
0,7
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 125.
H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups. Ergebnisse der Mathematik und Ihrer Grenzgebiete, New Series, no.14. Springer Verlag, 1957, Table 10.
L. Smith, Polynomial Invariants of Finite Groups, Peters, 1995, p. 199 (No. 35).
LINKS
T. D. Noe, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 248
Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,1,1,-1,0,1,-1,-2,1,0,-3,0,2,-1,-1,3,1,-2,1,3,-1,-1,2,0,-3,0,1,-2,-1,1,0,-1,1,1,0,0,1,0,-1).
FORMULA
G.f.: 1/((1-x^2)*(1-x^5)*(1-x^6)*(1-x^8)*(1-x^9)*(1-x^12)).
a(n) ~ 1/6220800*n^5 + 1/414720*n^4. - Ralf Stephan, Apr 29 2014
MAPLE
seq(coeff(series(1/((1-x^2)*(1-x^5)*(1-x^6)*(1-x^8)*(1-x^9)*(1-x^12)), x, n+1), x, n), n = 0..60); # G. C. Greubel, Jan 31 2020
MATHEMATICA
CoefficientList[Series[1/((1-x^2)(1-x^5)(1-x^6)(1-x^8)(1-x^9)(1-x^12)), {x, 0, 55}], x] (* Harvey P. Dale, Aug 10 2011 *)
PROG
(Magma) MolienSeries(CoxeterGroup("E6")); // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
(PARI) my(x='x+O('x^60)); Vec(1/((1-x^2)*(1-x^5)*(1-x^6)*(1-x^8)*(1-x^9)*(1-x^12))) \\ G. C. Greubel, Jan 31 2020
(Sage)
def A008584_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/((1-x^2)*(1-x^5)*(1-x^6)*(1-x^8)*(1-x^9)*(1-x^12)) ).list()
A008584_list(60) # G. C. Greubel, Jan 31 2020
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved