A008753 Expansion of (1+x^10)/((1-x)*(1-x^2)*(1-x^3)).

1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 15, 17, 21, 24, 28, 32, 37, 41, 47, 52, 58, 64, 71, 77, 85, 92, 100, 108, 117, 125, 135, 144, 154, 164, 175, 185, 197, 208, 220, 232, 245, 257, 271, 284, 298, 312, 327, 341

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).

Formula

a(n) = (6*(n-2)^2 + 143 + 4*cos(2*n*Pi/3) + 4*sqrt(3)*sin(2*n*Pi/3) + 9*(-1)^n)/36 for n >= 5. - G. C. Greubel, Aug 04 2019

Mathematica

CoefficientList[Series[(1+x^10)/(1-x)/(1-x^2)/(1-x^3), {x, 0, 60}], x] (* Harvey P. Dale, Jan 30 2013 *)
Join[{1, 1, 2, 3, 4}, Table[(6*(n-2)^2 +143 +4*Cos[2*n*Pi/3] + 4*Sqrt[3]* Sin[2*n*Pi/3] +9*(-1)^n)/36, {n, 5, 60}]] (* G. C. Greubel, Aug 04 2019 *)

Prog

(PARI) my(x='x+O('x^60)); Vec((1+x^10)/((1-x)*(1-x^2)*(1-x^3))) \\ G. C. Greubel, Aug 04 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^10)/((1-x)*(1-x^2)*(1-x^3)) )); // G. C. Greubel, Aug 04 2019
(Sage) ((1+x^10)/((1-x)*(1-x^2)*(1-x^3))).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Aug 04 2019
(GAP) a:=[7, 8, 10, 12, 15, 17];; 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], a); # G. C. Greubel, Aug 04 2019

Crossrefs

Sequence in context: A029005 A132154 A049807 * A029004 A332728 A008752

Adjacent sequences: A008750 A008751 A008752 * A008754 A008755 A008756

Keyword

nonn

Author

N. J. A. Sloane

Status

approved