A008726 Molien series 1/((1-x)^2*(1-x^8)) for 3-dimensional group [2,n] = *22n.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 18, 20, 22, 24, 27, 30, 33, 36, 39, 42, 45, 48, 52, 56, 60, 64, 68, 72, 76, 80, 85, 90, 95, 100, 105, 110, 115, 120, 126, 132, 138, 144, 150, 156, 162, 168, 175, 182, 189, 196, 203, 210, 217, 224, 232, 240, 248, 256, 264, 272, 280

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 191

Index entries for Molien series

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

Formula

G.f.: 1/((1-x)^2*(1-x^8)).

From Mitch Harris, Sep 08 2008: (Start)

a(n) = Sum_{j=0..n+8} floor(j/8).

a(n-8) = (1/2)*floor(n/8)*(2*n-6-8*floor(n/8)). (End)

a(n) = 2*a(n-1) - a(n-2) + a(n-8) - 2*a(n-9) + a(n-10). - R. J. Mathar, Apr 20 2010

Maple

seq(coeff(series(1/(1-x)^2/(1-x^8), x, n+1), x, n), n=0..80);

Mathematica

CoefficientList[Series[1/((1-x)^2*(1-x^8)), {x, 0, 80}], x] (* Vincenzo Librandi, Jun 11 2013 *)
LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, 1, -2, 1}, {1, 2, 3, 4, 5, 6, 7, 8, 10, 12}, 80] (* Harvey P. Dale, Jan 07 2015 *)

Prog

(PARI) my(x='x+O('x^80)); Vec(1/((1-x)^2*(1-x^8))) \\ G. C. Greubel, Sep 09 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( 1/((1-x)^2*(1-x^8)) )); // G. C. Greubel, Sep 09 2019
(Sage)
def A008726_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P(1/((1-x)^2*(1-x^8))).list()
A008726_list(80) # G. C. Greubel, Sep 09 2019
(GAP) a:=[1, 2, 3, 4, 5, 6, 7, 8, 10, 12];; for n in [11..80] do a[n]:=2*a[n-1] -a[n-2]+a[n-8]-2*a[n-9]+a[n-10]; od; a; # G. C. Greubel, Sep 09 2019

Crossrefs

Cf. A001840, A001972, A008724, A008725, A008732. - Vladimir Joseph Stephan Orlovsky, Mar 14 2010

Sequence in context: A122936 A330729 A118729 * A302834 A022788 A141340

Adjacent sequences: A008723 A008724 A008725 * A008727 A008728 A008729

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Mar 14 2010

Minor edits by Jon E. Schoenfield, Mar 28 2014

Status

approved