A008735 Molien series for 3-dimensional group [2+,n ] = 2*(n/2).

1, 0, 2, 0, 3, 0, 4, 1, 5, 2, 6, 3, 8, 4, 10, 5, 12, 6, 14, 8, 16, 10, 18, 12, 21, 14, 24, 16, 27, 18, 30, 21, 33, 24, 36, 27, 40, 30, 44, 33, 48, 36, 52, 40, 56, 44, 60, 48, 65, 52, 70, 56, 75, 60, 80, 65, 85, 70, 90

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Index entries for Molien series

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

Formula

G.f.: (1+x^7)/((1-x^2)^2*(1-x^12)).

a(n)= +a(n-1) +a(n-2) -a(n-3) +a(n-12) -a(n-13) -a(n-14) +a(n-15). - R. J. Mathar, Dec 18 2014

Maple

seq(coeff(series((1+x^7)/((1-x^2)^2*(1-x^12)), x, n+1), x, n), n = 0 .. 70); # modified by G. C. Greubel, Jul 30 2019

Mathematica

CoefficientList[Series[(1+x^7)/((1-x^2)^2*(1-x^12)), {x, 0, 70}], x] (* G. C. Greubel, Jul 30 2019 *)
LinearRecurrence[{1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1}, {1, 0, 2, 0, 3, 0, 4, 1, 5, 2, 6, 3, 8, 4, 10}, 60] (* Harvey P. Dale, Aug 10 2019 *)

Prog

(PARI) my(x='x+O('x^70)); Vec((1+x^7)/((1-x^2)^2*(1-x^12))) \\ G. C. Greubel, Jul 30 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+x^7)/((1-x^2)^2*(1-x^12)) )); // G. C. Greubel, Jul 30 2019
(Sage) ((1+x^7)/((1-x^2)^2*(1-x^12))).series(x, 70).coefficients(x, sparse=False) # G. C. Greubel, Jul 30 2019
(GAP) a:=[1, 0, 2, 0, 3, 0, 4, 1, 5, 2, 6, 3, 8, 4, 10];; for n in [16..70] do a[n]:=a[n-1]+a[n-2]-a[n-3]+a[n-12]-a[n-13]-a[n-14]+a[n-15]; od; a; # G. C. Greubel, Jul 30 2019

Crossrefs

Sequence in context: A008743 A029179 A008721 * A239241 A263395 A240139

Adjacent sequences: A008732 A008733 A008734 * A008736 A008737 A008738

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved