A008736 Molien series for 3-dimensional group [2+,n] = 2*(n/2).

1, 0, 2, 0, 3, 0, 4, 0, 5, 1, 6, 2, 7, 3, 8, 4, 10, 5, 12, 6, 14, 7, 16, 8, 18, 10, 20, 12, 22, 14, 24, 16, 27, 18, 30, 20, 33, 22, 36, 24, 39, 27, 42, 30, 45, 33, 48, 36, 52, 39, 56, 42, 60, 45, 64, 48, 68, 52, 72, 56

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, 0, 0, 0, 0, 1, -1, -1, 1).

Formula

G.f.: (1+x^9)/((1-x^2)^2*(1-x^16)).

Maple

seq(coeff(series((1+x^9)/((1-x^2)^2*(1-x^16)), x, n+1), x, n), n = 0 .. 70); # modified by G. C. Greubel, Jul 30 2019

Mathematica

CoefficientList[Series[(1+x^9)/((1-x^2)^2*(1-x^16)), {x, 0, 70}], x] (* G. C. Greubel, Jul 30 2019 *)
LinearRecurrence[{1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1}, {1, 0, 2, 0, 3, 0, 4, 0, 5, 1, 6, 2, 7, 3, 8, 4, 10, 5, 12}, 70] (* Harvey P. Dale, Oct 03 2020 *)

Prog

(PARI) my(x='x+O('x^70)); Vec((1+x^9)/((1-x^2)^2*(1-x^16))) \\ G. C. Greubel, Jul 30 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+x^9)/((1-x^2)^2*(1-x^16)) )); // G. C. Greubel, Jul 30 2019
(Sage) ((1+x^9)/((1-x^2)^2*(1-x^16))).series(x, 70).coefficients(x, sparse=False) # G. C. Greubel, Jul 30 2019
(GAP) a:=[1, 0, 2, 0, 3, 0, 4, 0, 5, 1, 6, 2, 7, 3, 8, 4, 10, 5, 12];; for n in [20..70] do a[n]:=a[n-1]+a[n-2]-a[n-3]+a[n-16]-a[n-17]-a[n-18]+a[n-19]; od; a; # G. C. Greubel, Jul 30 2019

Crossrefs

Sequence in context: A008803 A349375 A008722 * A263396 A029180 A008802

Adjacent sequences: A008733 A008734 A008735 * A008737 A008738 A008739

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved