A008728 Molien series for 3-dimensional group [2,n ] = *22n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 217, 224, 231, 238

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

a(n) = A179052(n) for n < 100. - Reinhard Zumkeller, Jun 27 2010

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 193
• Index entries for Molien series
• Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1).

Crossrefs

Cf. A001840, A001972, A008724, A008725, A008726, A008727, A008732.

Programs

GAP

a:=[1,2,3,4,5,6,7,8,9,10,12,14];; for n in [13..70] do a[n]:=2*a[n-1]-a[n-2]+a[n-10]-2*a[n-11]+a[n-12]; od; a; # G. C. Greubel, Jul 30 2019

Magma

R:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/((1-x)^2*(1-x^10)) )); // G. C. Greubel, Jul 30 2019

Maple

g:= 1/((1-x)^2*(1-x^10)); gser:= series(g, x=0,72); seq(coeff(gser, x, n), n=0..70); # modified by G. C. Greubel, Jul 30 2019

Mathematica

CoefficientList[Series[1/((1-x)^2(1-x^10)), {x,0,70}], x] (* Vincenzo Librandi, Jun 11 2013 *)

PARI

my(x='x+O('x^70)); Vec(1/((1-x)^2*(1-x^10))) \\ G. C. Greubel, Jul 30 2019

Sage

(1/((1-x)^2*(1-x^10))).series(x, 70).coefficients(x, sparse=False) # G. C. Greubel, Jul 30 2019

Formula

G.f.: 1/((1-x)^2*(1-x^10)).

From Mitch Harris, Sep 08 2008: (Start)

a(n) = Sum_{j=0..n+10} floor(j/10).

a(n-10) = (1/2)*floor(n/10)*(2*n - 8 - 10*floor(n/10)). (End)

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Mar 14 2010