A008752 Expansion of (1+x^9)/((1-x)*(1-x^2)*(1-x^3)).

1, 1, 2, 3, 4, 5, 7, 8, 10, 13, 15, 18, 22, 25, 29, 34, 38, 43, 49, 54, 60, 67, 73, 80, 88, 95, 103, 112, 120, 129, 139, 148, 158, 169, 179, 190, 202, 213, 225, 238, 250, 263, 277, 290, 304, 319, 333, 348

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,-2,1).

Mathematica

CoefficientList[Series[(1+x^9)/((1-x)*(1-x^2)*(1-x^3)), {x, 0, 50}], x] (* G. C. Greubel, Aug 04 2019 *)
LinearRecurrence[{2, -1, 1, -2, 1}, {1, 1, 2, 3, 4, 5, 7, 8, 10}, 50] (* Harvey P. Dale, Oct 24 2020 *)

Prog

(PARI) my(x='x+O('x^50)); Vec((1+x^9)/((1-x)*(1-x^2)*(1-x^3))) \\ G. C. Greubel, Aug 04 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+x^9)/((1-x)*(1-x^2)*(1-x^3)) )); // G. C. Greubel, Aug 04 2019
(Sage) ((1+x^9)/((1-x)*(1-x^2)*(1-x^3))).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Aug 04 2019
(GAP) a:=[1, 1, 2, 3, 4];; for n in [6..50] do a[n]:=2*a[n-1]-a[n-2]+a[n-3] -2*a[n-4]+a[n-5]; od; a; # G. C. Greubel, Aug 04 2019

Crossrefs

Sequence in context: A008753 A029004 A332728 * A029003 A339279 A034296

Adjacent sequences: A008749 A008750 A008751 * A008753 A008754 A008755

Keyword

nonn

Author

N. J. A. Sloane

Status

approved