OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,0,1,-1,-1,1).
FORMULA
G.f.: (1+x^7)/((1-x^2)^2*(1-x^6)).
a(n) = floor((n^2+3*n+21+7*(n+1)*(-1)^n)/24). - Tani Akinari, Jul 25 2013
G.f.: (1 -x +x^2 -x^3 +x^4 -x^5 +x^6)/( (1+x+x^2)*(1-x+x^2)*(1+x)^2*(1-x)^3 ). - R. J. Mathar, Dec
18 2014
MAPLE
seq(coeff(series((1+x^7)/((1-x^2)^2*(1-x^6)), x, n+1), x, n), n = 0..80);
MATHEMATICA
CoefficientList[Series[(1+x^7)/((1-x^2)^2*(1-x^6)), {x, 0, 80}], x] (* G. C. Greubel, Sep 12 2019 *)
LinearRecurrence[{1, 1, -1, 0, 0, 1, -1, -1, 1}, {1, 0, 2, 0, 3, 0, 5, 1, 7}, 80] (* Harvey P. Dale, Apr 16 2022 *)
PROG
(PARI) my(x='x+O('x^80)); Vec((1+x^7)/((1-x^2)^2*(1-x^6))) \\ G. C. Greubel, Sep 12 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1+x^7)/((1-x^2)^2*(1-x^6)) )); // G. C. Greubel, Sep 12 2019
(Sage)
def A008799_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1+x^7)/((1-x^2)^2*(1-x^6))).list()
A008799_list(80) # G. C. Greubel, Sep 12 2019
(GAP) a:=[1, 0, 2, 0, 3, 0, 5, 1, 7];; for n in [10..80] do a[n]:=a[n-1]+a[n-2]-a[n-3]+a[n-6]-a[n-7]-a[n-8]+a[n-9]; od; a; # G. C. Greubel, Sep 12 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition clarified by N. J. A. Sloane, Feb 02 2018
More terms added by G. C. Greubel, Sep 12 2019
STATUS
approved