A008820 Expansion of (1+2*x^7+x^12)/((1-x^2)^2*(1-x^12)).

1, 0, 2, 0, 3, 0, 4, 2, 5, 4, 6, 6, 9, 8, 12, 10, 15, 12, 18, 16, 21, 20, 24, 24, 29, 28, 34, 32, 39, 36, 44, 42, 49, 48, 54, 54, 61, 60, 68, 66, 75, 72, 82, 80, 89, 88, 96, 96, 105, 104, 114, 112, 123, 120, 132, 130, 141, 140, 150, 150, 161, 160, 172, 170, 183, 180, 194, 192, 205, 204

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

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), this sequence (m=3), A008821 (m=4).

Sequence in context: A274096 A318518 A008808 * A357475 A066682 A239968

Adjacent sequences: A008817 A008818 A008819 * A008821 A008822 A008823

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved