A008761 Expansion of (1+x^18)/((1-x)*(1-x^2)*(1-x^3)).

1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19, 21, 24, 27, 30, 33, 38, 41, 46, 51, 56, 61, 68, 73, 80, 87, 94, 101, 110, 117, 126, 135, 144, 153, 164, 173, 184, 195, 206, 217, 230, 241, 254, 267, 280, 293, 308

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,-1,-1,1).

Maple

seq(coeff(series((1+x^18)/((1-x)*(1-x^2)*(1-x^3)), x, n+1), x, n), n = 0 .. 40); # G. C. Greubel, Aug 09 2019

Mathematica

Join[{1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19}, LinearRecurrence[{1, 1, 0, -1, -1, 1}, {21, 24, 27, 30, 33, 38}, 47]] (* G. C. Greubel, Aug 09 2019 *)
CoefficientList[Series[(1+x^18)/((1-x)(1-x^2)(1-x^3)), {x, 0, 70}], x] (* Harvey P. Dale, Jun 06 2021 *)

Prog

(PARI) my(x='x+O('x^60)); Vec((1+x^18)/((1-x)*(1-x^2)*(1-x^3))) \\ G. C. Greubel, Aug 09 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^18)/((1-x)*(1-x^2)*(1-x^3)) )); // G. C. Greubel, Aug 09 2019
(Sage)
def A008761_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^18)/((1-x)*(1-x^2)*(1-x^3))).list()
A008761_list(60) # G. C. Greubel, Aug 09 2019
(GAP) a:=[21, 24, 27, 30, 33, 38];; for n in [7..60] do a[n]:=a[n-1]+a[n-2]-a[n-4]-a[n-5]+a[n-6]; od; Concatenation([1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19], a); # G. C. Greubel, Aug 09 2019

Crossrefs

Sequence in context: A211540 A001399 A069905 * A008760 A008759 A008758

Adjacent sequences: A008758 A008759 A008760 * A008762 A008763 A008764

Keyword

nonn

Author

N. J. A. Sloane

Status

approved