A008756 Expansion of (1+x^13)/((1-x)*(1-x^2)*(1-x^3)).

1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19, 22, 25, 29, 33, 37, 42, 47, 52, 58, 64, 70, 77, 84, 91, 99, 107, 115, 124, 133, 142, 152, 162, 172, 183, 194, 205, 217, 229, 241, 254, 267, 280, 294, 308, 322

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) = (92 - 15*(n+1) + 3*A000217(n+1) + A061347(n+1))/9 for n > 7. - R. J. Mathar, Feb 19 2008

Mathematica

CoefficientList[Series[(1+x^13)/((1-x)*(1-x^2)*(1-x^3)), {x, 0, 60}], x] (* G. C. Greubel, Aug 04 2019 *)

Prog

(PARI) my(x='x+O('x^60)); Vec((1+x^13)/((1-x)*(1-x^2)*(1-x^3))) \\ G. C. Greubel, Aug 04 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^13)/((1-x)*(1-x^2)*(1-x^3)) )); // G. C. Greubel, Aug 04 2019
(Sage) ((1+x^13)/((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, 19];; for n in [7..60] 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], a); # G. C. Greubel, Aug 04 2019

Crossrefs

Cf. A000217, A061347.

Sequence in context: A008758 A370747 A008757 * A008755 A029006 A085756

Adjacent sequences: A008753 A008754 A008755 * A008757 A008758 A008759

Keyword

nonn

Author

N. J. A. Sloane

Status

approved