A008723 Molien series for 3-dimensional group [2,11] = *2 2 11.

1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 1, 7, 2, 8, 3, 9, 4, 10, 5, 11, 6, 13, 7, 15, 8, 17, 9, 19, 10, 21, 11, 23, 13, 25, 15, 27, 17, 29, 19, 31, 21, 33, 23, 36, 25, 39, 27, 42, 29, 45, 31, 48, 33, 51, 36, 54, 39, 57, 42, 60

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 226

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1,0,0,0,0,0,0,1,0,-2,0,1).

Formula

G.f.: 1/((1-x^2)^2*(1-x^11)).

a(n) ~ 1/88*n^2. - Ralf Stephan, Apr 29 2014

Maple

seq(coeff(series(1/((1-x^2)^2*(1-x^11)), x, n+1), x, n), n = 0 .. 80); # G. C. Greubel, Sep 09 2019

Mathematica

CoefficientList[Series[1/(1-x^2)^2/(1-x^11), {x, 0, 80}], x] (* Wesley Ivan Hurt, Mar 30 2017 *)
LinearRecurrence[{0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 1}, {1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 1, 7, 2, 8}, 70] (* Harvey P. Dale, Jun 22 2019 *)

Prog

(PARI) my(x='x+O('x^80)); Vec(1/((1-x^2)^2*(1-x^11))) \\ G. C. Greubel, Sep 09 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( 1/((1-x^2)^2*(1-x^11)) )); // G. C. Greubel, Sep 09 2019
(Sage)
def A008723_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P(1/((1-x^2)^2*(1-x^11))).list()
A008723_list(80) # G. C. Greubel, Sep 09 2019
(GAP) a:=[1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 1, 7, 2, 8];; for n in [16..80] do a[n]:=2*a[n-2]-a[n-4]+a[n-11]-2*a[n-13]+a[n-15]; od; a; # G. C. Greubel, Sep 09 2019

Crossrefs

Sequence in context: A326834 A034948 A135472 * A263397 A008803 A349375

Adjacent sequences: A008720 A008721 A008722 * A008724 A008725 A008726

Keyword

nonn

Author

N. J. A. Sloane

Status

approved