A008821 Expansion of (1+2*x^9+x^16)/((1-x^2)^2*(1-x^16)).

1, 0, 2, 0, 3, 0, 4, 0, 5, 2, 6, 4, 7, 6, 8, 8, 11, 10, 14, 12, 17, 14, 20, 16, 23, 20, 26, 24, 29, 28, 32, 32, 37, 36, 42, 40, 47, 44, 52, 48, 57, 54, 62, 60, 67, 66, 72, 72, 79, 78, 86, 84, 93, 90, 100, 96, 107, 104, 114, 112, 121, 120, 128, 128, 137, 136

Offset

0,3

Links

Table of n, a(n) for n=0..65.

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

Formula

G.f.: (1+2*x^9+x^16)/((1-x^2)^2*(1-x^16)). - G. C. Greubel, Sep 13 2019

G.f.: (1-x+x^2-x^3+x^4-x^5+x^6-x^7+x^8+x^9-x^10+x^11-x^12+x^13-x^14+x^15)/((1-x)^3*(1+x)^2*(1+x^2)*(1+x^4)*(1+x^8)). - R. J. Mathar, Feb 04 2022

Maple

seq(coeff(series((1+2*x^9+x^16)/((1-x^2)^2*(1-x^16)), x, n+1), x, n), n = 0..75); # G. C. Greubel, Sep 13 2019

Mathematica

CoefficientList[Series[(1+2*x^9+x^16)/((1-x^2)^2*(1-x^16)), {x, 0, 75}], x] (* or *) LinearRecurrence[{1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1}, {1, 0, 2, 0, 3, 0, 4, 0, 5, 2, 6, 4, 7, 6, 8, 8, 11, 10, 14}, 75] (* G. C. Greubel, Sep 13 2019 *)

Prog

(PARI) my(x='x+O('x^75)); Vec((1+2*x^9+x^16)/((1-x^2)^2*(1-x^16))) \\ G. C. Greubel, Sep 13 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 75); Coefficients(R!( (1+2*x^9+x^16)/((1-x^2)^2*(1-x^16)) )); // G. C. Greubel, Sep 13 2019
(Sage)
def A008821_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+2*x^9+x^16)/((1-x^2)^2*(1-x^16))).list()
A008821_list(75) # G. C. Greubel, Sep 13 2019
(GAP) a:=[1, 0, 2, 0, 3, 0, 4, 0, 5, 2, 6, 4, 7, 6, 8, 8, 11, 10, 14];; for n in [20..75] do a[n]:=a[n-1]+a[n-2]-a[n-3]+a[n-16]-a[n-17]-a[n-18]+a[n-19]; od; a; # G. C. Greubel, Sep 13 2019

Crossrefs

Expansions of the form (1 +2*x^(2*m+1) +x^(4*m))/((1-x^2)^2*(1-x^(4*m))): A008818 (m=1), A008819 (m=2), A008820 (m=3), this sequence (m=4).

Sequence in context: A029180 A008802 A008809 * A194749 A284969 A097852

Adjacent sequences: A008818 A008819 A008820 * A008822 A008823 A008824

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms added by G. C. Greubel, Sep 13 2019

Status

approved