OFFSET
0,7
COMMENTS
The relevant generating function is 1/((1-z^2)*(1-z^12)*(1-z^20)*(1-z^30)) and is reduced with x=z^2 below to indicate that the intermediate zeros are not listed.
Number of partitions into parts 1, 6, 10, and 15. - Joerg Arndt, Apr 29 2014
REFERENCES
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. 30).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Roberto De Maria Nunes Mendes, Symmetries of spherical harmonics, Transactions of the American Mathematical Society 204 (1975): 161-178. See subgroup 68.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 240
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 0, 1, -2, 1, 0, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1).
FORMULA
G.f.: 1/((1-x)*(1-x^6)*(1-x^10)*(1-x^15)). - M. F. Hasler, Mar 26 2012
a(n) ~ 1/5400*n^3. - Ralf Stephan, Apr 29 2014
MAPLE
seq(coeff(series(1/((1-x)*(1-x^6)*(1-x^10)*(1-x^15)), x, n+1), x, n), n = 0 .. 80); # G. C. Greubel, Sep 08 2019
MATHEMATICA
CoefficientList[Series[1/((1-x)*(1-x^6)*(1-x^10)*(1-x^15)), {x, 0, 80}], x] (* G. C. Greubel, Sep 08 2019 *)
PROG
(PARI) A008668_list = n -> Vec(1/((1-x)*(1-x^6)*(1-x^10)*(1-x^15)) +O(x^n)) \\ M. F. Hasler, Mar 26 2012
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( 1/((1-x)*(1-x^6)*(1-x^10)*(1-x^15)) )); // G. C. Greubel, Sep 08 2019
(Sage)
def A008668_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P(1/((1-x)*(1-x^6)*(1-x^10)*(1-x^15))).list()
A008668_list(80) # G. C. Greubel, Sep 08 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(61) onward added by G. C. Greubel, Sep 08 2019
STATUS
approved