A008819 Expansion of (1+2*x^5+x^8)/((1-x^2)^2*(1-x^8)).

1, 0, 2, 0, 3, 2, 4, 4, 7, 6, 10, 8, 13, 12, 16, 16, 21, 20, 26, 24, 31, 30, 36, 36, 43, 42, 50, 48, 57, 56, 64, 64, 73, 72, 82, 80, 91, 90, 100, 100, 111, 110, 122, 120, 133, 132, 144, 144, 157, 156, 170, 168, 183, 182, 196, 196, 211, 210, 226, 224, 241, 240

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

Cf. Expansions of the form (1 +2*x^(2*m+1) +x^(4*m))/((1-x^2)^2*(1-x^(4*m))): A008818 (m=1), this sequence (m=2), A008820 (m=3), A008821 (m=4).

Sequence in context: A291273 A008807 A263149 * A374018 A279591 A279675

Adjacent sequences: A008816 A008817 A008818 * A008820 A008821 A008822

Keyword

nonn

Author

N. J. A. Sloane

Status

approved