A008750 Expansion of (1+x^7)/((1-x)*(1-x^2)*(1-x^3)).

1, 1, 2, 3, 4, 5, 7, 9, 11, 14, 17, 20, 24, 28, 32, 37, 42, 47, 53, 59, 65, 72, 79, 86, 94, 102, 110, 119, 128, 137, 147, 157, 167, 178, 189, 200, 212, 224, 236, 249, 262, 275, 289, 303, 317, 332, 347, 362

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) = A001399(n) + A001399(n-7). - R. J. Mathar, Jul 09 2015

Mathematica

CoefficientList[Series[(1+x^7)/(1-x)/(1-x^2)/(1-x^3), {x, 0, 50}], x] (* Michael De Vlieger, Jul 09 2015 *)

Prog

(PARI) my(x='x+O('x^50)); Vec((1+x^7)/((1-x)*(1-x^2)*(1-x^3))) \\ G. C. Greubel, Aug 04 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+x^7)/((1-x)*(1-x^2)*(1-x^3)) )); // G. C. Greubel, Aug 04 2019
(Sage) ((1+x^7)/((1-x)*(1-x^2)*(1-x^3))).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Aug 04 2019
(GAP) a:=[1, 1, 2, 3, 4];; for n in [6..50] do a[n]:=2*a[n-1]-a[n-2]+a[n-3] -2*a[n-4]+a[n-5]; od; a; # G. C. Greubel, Aug 04 2019

Crossrefs

Cf. A001399.

Sequence in context: A286267 A337334 A375606 * A076677 A029001 A161306

Adjacent sequences: A008747 A008748 A008749 * A008751 A008752 A008753

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved