OFFSET
0,3
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,0,0,0,1,-1,-1,1).
FORMULA
a(0)=1, a(1)=0, a(2)=2, a(3)=0, a(4)=3, a(5)=2, a(6)=4, a(7)=4, a(8)=7, a(9)=6, a(10)=10, a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-8) - a(n-9) - a(n-10) + a(n-11). - Harvey P. Dale, Oct 28 2015
MAPLE
seq(coeff(series((1+2*x^5+x^8)/((1-x^2)^2*(1-x^8)), x, n+1), x, n), n = 0..60); # G. C. Greubel, Sep 12 2019
MATHEMATICA
CoefficientList[Series[(1+2x^5+x^8)/(1-x^2)^2/(1-x^8), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, 1, -1, 0, 0, 0, 0, 1, -1, -1, 1}, {1, 0, 2, 0, 3, 2, 4, 4, 7, 6, 10}, 60] (* Harvey P. Dale, Oct 28 2015 *)
PROG
(PARI) my(x='x+O('x^60)); Vec((1+2*x^5+x^8)/((1-x^2)^2*(1-x^8))) \\ G. C. Greubel, Sep 12 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+2*x^5+x^8)/((1-x^2)^2*(1-x^8)) )); // G. C. Greubel, Sep 12 2019
(Sage)
def A008819_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1+2*x^5+x^8)/((1-x^2)^2*(1-x^8))).list()
A008819_list(60) # G. C. Greubel, Sep 12 2019
(GAP) a:=[1, 0, 2, 0, 3, 2, 4, 4, 7, 6, 10];; for n in [12..60] do a[n]:=a[n-1] +a[n-2]-a[n-3]+a[n-8]-a[n-9]-a[n-10]+a[n-11]; od; a; # G. C. Greubel, Sep 12 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved