login
A008800
Molien series for group [2,7]+ = 227.
1
1, 0, 2, 0, 3, 0, 4, 1, 6, 2, 8, 3, 10, 4, 13, 6, 16, 8, 19, 10, 22, 13, 26, 16, 30, 19, 34, 22, 39, 26, 44, 30, 49, 34, 54, 39, 60, 44, 66, 49, 72, 54, 79, 60, 86, 66, 93, 72, 100, 79, 108, 86, 116, 93, 124, 100, 133, 108, 142, 116, 151, 124, 160, 133, 170, 142, 180, 151, 190, 160, 201, 170
OFFSET
0,3
FORMULA
G.f.: (1+x^8)/((1-x^2)^2 * (1-x^7)).
MAPLE
seq(coeff(series((1+x^8)/((1-x^2)^2*(1-x^7)), x, n+1), x, n), n = 0..80);
MATHEMATICA
CoefficientList[Series[(1+x^8)/((1-x^2)^2*(1-x^7)), {x, 0, 80}], x] (* G. C. Greubel, Sep 12 2019 *)
LinearRecurrence[{0, 2, 0, -1, 0, 0, 1, 0, -2, 0, 1}, {1, 0, 2, 0, 3, 0, 4, 1, 6, 2, 8}, 80] (* Harvey P. Dale, Jul 07 2021 *)
PROG
(PARI) my(x='x+O('x^80)); Vec((1+x^8)/((1-x^2)^2*(1-x^7))) \\ G. C. Greubel, Sep 12 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1+x^8)/((1-x^2)^2*(1-x^7)) )); // G. C. Greubel, Sep 12 2019
(Sage)
def A008800_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1+x^8)/((1-x^2)^2*(1-x^7))).list()
A008800_list(80) # G. C. Greubel, Sep 12 2019
(GAP) a:=[1, 0, 2, 0, 3, 0, 4, 1, 6, 2, 8];; for n in [12..80] do a[n]:=2*a[n-2] -a[n-4]+a[n-7]-2*a[n-9]+a[n-11]; od; a; # G. C. Greubel, Sep 12 2019
CROSSREFS
Sequence in context: A263395 A240139 A360952 * A274096 A318518 A008808
KEYWORD
nonn
EXTENSIONS
Definition clarified by N. J. A. Sloane, Feb 02 2018
More terms added by G. C. Greubel, Sep 12 2019
STATUS
approved