A008816 Expansion of (1+x^9)/((1-x)^2*(1-x^9)).

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 88, 95, 102, 109, 116, 123, 130, 137, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 236, 247, 258, 269, 280, 291, 302, 313, 324, 337, 350, 363, 376, 389, 402

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,1,-2,1).

Formula

G.f.: (1+x^9)/((1-x)^2*(1-x^9)). - G. C. Greubel, Sep 12 2019

Maple

seq(coeff(series((1+x^9)/((1-x)^2*(1-x^9)), x, n+1), x, n), n = 0..50); # G. C. Greubel, Sep 12 2019

Mathematica

LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, 0, 1, -2, 1}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15}, 70] (* or *) CoefficientList[Series[(1+x^9)/((1-x)^2*(1-x^9)), {x, 0, 70}], x] (* G. C. Greubel, Sep 12 2019 *)

Prog

(PARI) my(x='x+O('x^70)); Vec((1+x^9)/((1-x)^2*(1-x^9))) \\ G. C. Greubel, Sep 12 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+x^9)/((1-x)^2*(1-x^9)) )); // G. C. Greubel, Sep 12 2019
(Sage)
def A008815_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^8)/((1-x)^2*(1-x^8))).list()
A008815_list(70) # G. C. Greubel, Sep 12 2019
(GAP) a:=[1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15];; for n in [12..70] do a[n]:=2*a[n-1] -a[n-2]+a[n-9]-2*a[n-10]+a[n-11]; od; a; # G. C. Greubel, Sep 12 2019

Crossrefs

Cf. Expansions of the form (1+x^m)/((1-x)^2*(1-x^m)): A000290 (m=1), A000982 (m=2), A008810 (m=3), A008811 (m=4), A008812 (m=5), A008813 (m=6), A008814 (m=7), A008815 (m=8), this sequence (m=9), A008817 (m=10).

Sequence in context: A116066 A261874 A334929 * A002271 A048381 A185186

Adjacent sequences: A008813 A008814 A008815 * A008817 A008818 A008819

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms added by G. C. Greubel, Sep 12 2019

Status

approved