A008803 Molien series for group [2,10]+ = 2 2 10.

1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 7, 1, 9, 2, 11, 3, 13, 4, 15, 5, 18, 7, 21, 9, 24, 11, 27, 13, 30, 15, 34, 18, 38, 21, 42, 24, 46, 27, 50, 30, 55, 34, 60, 38, 65, 42, 70, 46, 75, 50, 81, 55, 87, 60, 93, 65, 99, 70, 105, 75, 112, 81, 119, 87, 126, 93, 133, 99, 140, 105, 148, 112, 156, 119, 164

Offset

0,3

Links

G. C. Greubel, 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,-1,0,0,0,0,0,0,1,-1,-1,1).

Formula

G.f.: (1+x^11)/((1-x^2)^2*(1-x^10)) (from MAPLE line).

a(n) = floor((11*(2*n+3)*(-1)^n+2*n^2+6*n+79)/80). - Tani Akinari, Jul 25 2013

G.f.: (1 -x +x^2 -x^3 +x^4 -x^5 +x^6 -x^7 +x^8 -x^9)/( (1-x+x^2-x^3+x^4)* (1+x+x^2+x^3+x^4)*(1+x)^2*(1-x)^3 ). - R. J. Mathar, Dec 18 2014

Maple

seq(coeff(series((1+x^11)/((1-x^2)^2*(1-x^10)), x, n+1), x, n), n = 0..80);

Mathematica

LinearRecurrence[{1, 1, -1, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1}, {1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 7, 1, 9}, 80] (* Ray Chandler, Jul 15 2015 *)

Prog

(PARI) my(x='x+O('x^80)); Vec((1+x^11)/((1-x^2)^2*(1-x^10))) \\ G. C. Greubel, Sep 12 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1+x^11)/((1-x^2)^2*(1-x^10)) )); // G. C. Greubel, Sep 12 2019
(Sage)
def A008803_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^11)/((1-x^2)^2*(1-x^10))).list()
A008803_list(80) # G. C. Greubel, Sep 12 2019
(GAP) a:=[1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 7, 1, 9];; for n in [14..80] do a[n]:=a[n-1] +a[n-2]-a[n-3]+a[n-10]-a[n-11]-a[n-12]+a[n-13]; od; a; # G. C. Greubel, Sep 12 2019

Crossrefs

Sequence in context: A135472 A008723 A263397 * A349375 A008722 A008736

Adjacent sequences: A008800 A008801 A008802 * A008804 A008805 A008806

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved