A008755 Expansion of (1+x^12)/((1-x)*(1-x^2)*(1-x^3)).

1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 20, 22, 26, 30, 34, 38, 44, 48, 54, 60, 66, 72, 80, 86, 94, 102, 110, 118, 128, 136, 146, 156, 166, 176, 188, 198, 210, 222, 234, 246, 260, 272, 286, 300, 314, 328

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 -36*n +263 +9*(-1)^n +16*(-1)^n*cos(n*Pi/3))/36 for n >=7. - G. C. Greubel, Aug 04 2019

Mathematica

CoefficientList[Series[(1+x^12)/(1-x)/(1-x^2)/(1-x^3), {x, 0, 60}], x] (* Harvey P. Dale, Aug 27 2013 *)
Join[{1, 1, 2, 3, 4, 5, 7}, Table[(6*n^2 -36*n +263 +9*(-1)^n + 16*(-1)^n*Cos[n*Pi/3])/36, {n, 7, 60}]] (* G. C. Greubel, Aug 04 2019 *)

Prog

(PARI) my(x='x+O('x^60)); Vec((1+x^12)/((1-x)*(1-x^2)*(1-x^3))) \\ G. C. Greubel, Aug 04 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^12)/((1-x)*(1-x^2)*(1-x^3)) )); // G. C. Greubel, Aug 04 2019
(Sage) ((1+x^12)/((1-x)*(1-x^2)*(1-x^3))).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Aug 04 2019
(GAP) a:=[8, 10, 12, 14, 16, 20];; 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], a); # G. C. Greubel, Aug 04 2019

Crossrefs

Sequence in context: A370747 A008757 A008756 * A029006 A085756 A350896

Adjacent sequences: A008752 A008753 A008754 * A008756 A008757 A008758

Keyword

nonn

Author

N. J. A. Sloane

Status

approved