A008760 Expansion of (1+x^17)/((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, 34, 38, 42, 47, 52, 57, 63, 69, 75, 82, 89, 96, 104, 112, 120, 129, 138, 147, 157, 167, 177, 188, 199, 210, 222, 234, 246, 259, 272, 285, 299, 313

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).

Formula

G.f.: (1+x^17)/((1-x)*(1-x^2)*(1-x^3)).

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5). - Wesley Ivan Hurt, May 25 2024

Maple

seq(coeff(series((1+x^17)/((1-x)*(1-x^2)*(1-x^3)), x, n+1), x, n), n = 0 .. 60); # G. C. Greubel, Aug 09 2019

Mathematica

CoefficientList[Series[(1+x^17)/(1-x)/(1-x^2)/(1-x^3), {x, 0, 50}], x] (* Harvey P. Dale, Nov 30 2011 *)
Join[{1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16}, LinearRecurrence[{2, -1, 1, -2, 1}, {19, 21, 24, 27, 30}, 48]] (* G. C. Greubel, Aug 09 2019 *)

Prog

(PARI) my(x='x+O('x^60)); Vec((1+x^17)/((1-x)*(1-x^2)*(1-x^3))) \\ G. C. Greubel, Aug 09 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^17)/((1-x)*(1-x^2)*(1-x^3)) )); // G. C. Greubel, Aug 09 2019
(Sage)
def A008760_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x^17)/((1-x)*(1-x^2)*(1-x^3)) ).list()
A008760_list(60) # G. C. Greubel, Aug 09 2019
(GAP) a:=[19, 21, 24, 27, 30];; for n in [6..48] do a[n]:=2*a[n-1]-a[n-2] +a[n-3]-2*a[n-4]+a[n-5]; od; Concatenation([1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16], a); # G. C. Greubel, Aug 09 2019

Crossrefs

Sequence in context: A001399 A069905 A008761 * A008759 A008758 A370747

Adjacent sequences: A008757 A008758 A008759 * A008761 A008762 A008763

Keyword

nonn

Author

N. J. A. Sloane

Status

approved