A008770 Expansion of (1+x^9)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

1, 1, 2, 3, 5, 6, 9, 11, 15, 19, 24, 29, 37, 44, 53, 63, 75, 87, 102, 117, 135, 154, 175, 197, 223, 249, 278, 309, 343, 378, 417, 457, 501, 547, 596, 647, 703, 760, 821, 885, 953, 1023, 1098, 1175, 1257, 1342, 1431, 1523, 1621, 1721, 1826, 1935, 2049, 2166, 2289, 2415, 2547, 2683

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

Formula

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) - a(n-5) + a(n-6) - a(n-7) + 2*a(n-8) - a(n-9); a(0)=1, a(1)=1, a(2)=2, a(3)=3, a(4)=5, a(5)=6, a(6)=9, a(7)=11, a(8)=15. - Harvey P. Dale, Oct 02 2012

Maple

seq(coeff(series((1+x^9)/((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[(x^9+1)/(1-x)/(1-x^2)/(1-x^3)/(1-x^4), {x, 0, 60}], x] (* or *) LinearRecurrence[{2, -1, 1, -1, -1, 1, -1, 2, -1}, {1, 1, 2, 3, 5, 6, 9, 11, 15}, 60] (* Harvey P. Dale, Oct 02 2012 *)

Prog

(PARI) my(x='x+O('x^60)); Vec((1+x^9)/((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^9)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)) )); // G. C. Greubel, Sep 10 2019
(Sage)
def A008770_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^9)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))).list()
A008770_list(60) # G. C. Greubel, Sep 10 2019
(GAP) a:=[1, 1, 2, 3, 5, 6, 9, 11, 15];; for n in [10..60] do a[n]:=2*a[n-1]-a[n-2]+a[n-3]-a[n-4]-a[n-5]+a[n-6]-a[n-7]+2*a[n-8]-a[n-9]; od; a; # G. C. Greubel, Sep 10 2019

Crossrefs

Sequence in context: A008771 A309831 A309830 * A347548 A230515 A030068

Adjacent sequences: A008767 A008768 A008769 * A008771 A008772 A008773

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Terms a(45) onward added by G. C. Greubel, Sep 10 2019

Status

approved