A008758 Expansion of (1+x^15)/((1-x)*(1-x^2)*(1-x^3)).

1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19, 21, 24, 28, 31, 35, 40, 44, 49, 55, 60, 66, 73, 79, 86, 94, 101, 109, 118, 126, 135, 145, 154, 164, 175, 185, 196, 208, 219, 231, 244, 256, 269, 283, 296, 310

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

a(n) = (6*n^2 -54*n +452 + 8*(-1)^n*cos(n*Pi/3) + 8*cos(2*n*Pi/3))/36 for n>9. - G. C. Greubel, Aug 09 2019

Maple

seq(coeff(series((1+x^15)/((1-x)*(1-x^2)*(1-x^3)), x, n+1), x, n), n = 1 .. 60); # G. C. Greubel, Aug 09 2019

Mathematica

CoefficientList[Series[(1+x^15)/(1-x)/(1-x^2)/(1-x^3), {x, 0, 60}], x] (* Harvey P. Dale, Dec 28 2013 *)
Join[{1, 1, 2, 3, 4, 5, 7, 8, 10, 12}, Table[(6*n^2 -54*n +452 + 8*(-1)^n*Cos[n*Pi/3] + 8*Cos[2*n*Pi/3])/36, {n, 10, 60}]] (* G. C. Greubel, Aug 09 2019 *)

Prog

(PARI) my(x='x+O('x^60)); Vec((1+x^15)/((1-x)*(1-x^2)*(1-x^3))) \\ G. C. Greubel, Aug 09 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^15)/((1-x)*(1-x^2)*(1-x^3)) )); // G. C. Greubel, Aug 09 2019
(Sage)
def A008758_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x^15)/((1-x)*(1-x^2)*(1-x^3)) ).list()
A008758_list(60) # G. C. Greubel, Aug 09 2019
(GAP) a:=[14, 16, 19, 21, 24];; for n in [6..30] 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], a); # G. C. Greubel, Aug 09 2019

Crossrefs

Sequence in context: A008761 A008760 A008759 * A370747 A008757 A008756

Adjacent sequences: A008755 A008756 A008757 * A008759 A008760 A008761

Keyword

nonn

Author

N. J. A. Sloane

Status

approved