A008757 Expansion of (1+x^14)/((1-x)*(1-x^2)*(1-x^3)).

1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19, 21, 25, 28, 32, 36, 41, 45, 51, 56, 62, 68, 75, 81, 89, 96, 104, 112, 121, 129, 139, 148, 158, 168, 179, 189, 201, 212, 224, 236, 249, 261, 275, 288, 302, 316

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-4)^2 + 287 + 9*(-1)^n + 8*(-1)^n*cos((n-2)*Pi/3) + 8*cos(2*n*Pi/3))/36 for n >= 9. - G. C. Greubel, Aug 04 2019

Mathematica

CoefficientList[Series[(1+x^14)/(1-x)/(1-x^2)/(1-x^3), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, 1, 0, -1, -1, 1}, {1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19, 21, 25}, 60] (* Harvey P. Dale, Jul 27 2017 *)
Join[{1, 1, 2, 3, 4, 5, 7, 8, 10}, Table[(6*(n-4)^2 +287 +9*(-1)^n +8*(-1)^n*Cos[(n-2)*Pi/3] +8*Cos[2*n*Pi/3])/36, {n, 9, 60}]] (* G. C. Greubel, Aug 04 2019 *)

Prog

(PARI) my(x='x+O('x^60)); Vec((1+x^14)/((1-x)*(1-x^2)*(1-x^3))) \\ G. C. Greubel, Aug 04 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^14)/((1-x)*(1-x^2)*(1-x^3)) )); // G. C. Greubel, Aug 04 2019
(Sage) ((1+x^14)/((1-x)*(1-x^2)*(1-x^3))).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Aug 04 2019
(GAP) a:=[12, 14, 16, 19, 21, 25];; 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], a); # G. C. Greubel, Aug 04 2019

Crossrefs

Sequence in context: A008759 A008758 A370747 * A008756 A008755 A029006

Adjacent sequences: A008754 A008755 A008756 * A008758 A008759 A008760

Keyword

nonn

Author

N. J. A. Sloane

Status

approved