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,-1,0,0,0,0,0,0,0,0,1,-1,-1,1).
FORMULA
G.f.: (1+2*x^7+x^12)/((1-x^2)^2*(1-x^12)). - G. C. Greubel, Sep 12 2019
MAPLE
seq(coeff(series((1+2*x^7+x^12)/((1-x^2)^2*(1-x^12)), x, n+1), x, n), n = 0..75); # G. C. Greubel, Sep 12 2019
MATHEMATICA
CoefficientList[Series[(1+2*x^7+x^12)/((1-x^2)^2*(1-x^12)), {x, 0, 75}], x] (* or *) LinearRecurrence[{1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1}, {1, 0, 2, 0, 3, 0, 4, 2, 5, 4, 6, 6, 9, 8, 12}, 75] (* G. C. Greubel, Sep 12 2019 *)
PROG
(PARI) my(x='x+O('x^75)); Vec((1+2*x^7+x^12)/((1-x^2)^2*(1-x^12))) \\ G. C. Greubel, Sep 12 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 75); Coefficients(R!( (1+2*x^7+x^12)/((1-x^2)^2*(1-x^12)) )); // G. C. Greubel, Sep 12 2019
(Sage)
def A008820_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1+2*x^7+x^12)/((1-x^2)^2*(1-x^12))).list()
A008820_list(75) # G. C. Greubel, Sep 12 2019
(GAP) a:=[1, 0, 2, 0, 3, 0, 4, 2, 5, 4, 6, 6, 9, 8, 12];; for n in [16..75] 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, Sep 12 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms added by G. C. Greubel, Sep 12 2019
STATUS
approved