A008773 Expansion of (1+x^12)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

1, 1, 2, 3, 5, 6, 9, 11, 15, 18, 23, 27, 35, 40, 49, 57, 69, 78, 93, 105, 123, 138, 159, 177, 203, 224, 253, 279, 313, 342, 381, 415, 459, 498, 547, 591, 647, 696, 757, 813, 881, 942, 1017, 1085, 1167, 1242, 1331, 1413, 1511, 1600, 1705, 1803, 1917, 2022, 2145

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 (1,1,0,0,-2,0,0,1,1,-1).

Maple

seq(coeff(series((1+x^12)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)), x, n+1), x, n), n = 0 .. 60); # G. C. Greubel, Sep 10 2019

Mathematica

CoefficientList[Series[(1+x^12)/(1-x)/(1-x^2)/(1-x^3)/(1-x^4), {x, 0, 60}], x] (* Stefan Steinerberger, Apr 08 2006 *)
Join[{1, 1, 2}, LinearRecurrence[{1, 1, 0, 0, -2, 0, 0, 1, 1, -1}, {3, 5, 6, 9, 11, 15, 18, 23, 27, 35}, 60]] (* G. C. Greubel, Sep 10 2019 *)

Prog

(PARI) my(x='x+O('x^60)); Vec((1+x^12)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))) \\ G. C. Greubel, Sep 10 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^12)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)) )); // G. C. Greubel, Sep 10 2019
(Sage)
def A008773_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^12)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))).list()
A008773_list(60) # G. C. Greubel, Sep 10 2019
(GAP) a:=[3, 5, 6, 9, 11, 15, 18, 23, 27, 35];; for n in [11..60] do a[n]:=a[n-1] +a[n-2]-2*a[n-5]+a[n-8]+a[n-9]-a[n-10]; od; Concatenation([1, 1, 2], a); # G. C. Greubel, Sep 10 2019

Crossrefs

Sequence in context: A001400 A372703 A350897 * A008772 A351003 A008771

Adjacent sequences: A008770 A008771 A008772 * A008774 A008775 A008776

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Stefan Steinerberger, Apr 08 2006

Status

approved