OFFSET
0,4
COMMENTS
Number of partitions of n into parts 1, 3 or 9. - Reinhard Zumkeller, Aug 12 2011
REFERENCES
D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 219
Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, -1, 0, 0, 0, 0, 1, -1, 0, -1, 1).
FORMULA
G.f.: 1/((1-x)*(1-x^3)*(1-x^9)).
a(n) = floor((6*(floor(n/3) +1)*(3*floor(n/3) -n +1) +n^2 +13*n +58)/54). - Tani Akinari, Jul 12 2013
MAPLE
1/((1-x)*(1-x^3)*(1-x^9)): seq(coeff(series(%, x, n+1), x, n), n=0..70);
MATHEMATICA
CoefficientList[Series[1/((1-x)*(1-x^3)*(1-x^9)), {x, 0, 70}], x] (* G. C. Greubel, Sep 06 2019 *)
PROG
(PARI) my(x='x+O('x^70)); Vec(1/((1-x)*(1-x^3)*(1-x^9))) \\ G. C. Greubel, Sep 06 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/((1-x)*(1-x^3)*(1-x^9)) )); // G. C. Greubel, Sep 06 2019
(Sage)
def A008649_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P(1/((1-x)*(1-x^3)*(1-x^9))).list()
A008649_list(70) # G. C. Greubel, Sep 06 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved