A008751 Expansion of (1+x^8)/((1-x)*(1-x^2)*(1-x^3)).

1, 1, 2, 3, 4, 5, 7, 8, 11, 13, 16, 19, 23, 26, 31, 35, 40, 45, 51, 56, 63, 69, 76, 83, 91, 98, 107, 115, 124, 133, 143, 152, 163, 173, 184, 195, 207, 218, 231, 243, 256, 269, 283, 296, 311, 325, 340, 355

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,-1,1).

Crossrefs

Cf. A001399, A008747.

Programs

GAP

Concatenation([1,1,2], List([3..50], n-> Int(((n-1)^2 +17)/6))); # G. C. Greubel, Aug 04 2019

Magma

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+x^8)/((1-x)*(1-x^2)*(1-x^3)) )); // G. C. Greubel, Aug 04 2019

Mathematica

CoefficientList[Series[(1+x^8)/((1-x)(1-x^2)(1-x^3)),{x,0,50}],x] (* Vincenzo Librandi, Feb 25 2012 *)
Join[{1,1,2}, Floor[((Range[3, 50] -1)^2 +17)/6]] (* G. C. Greubel, Aug 04 2019 *)

PARI

my(x='x+O('x^50)); Vec((1+x^8)/((1-x)*(1-x^2)*(1-x^3))) \\ G. C. Greubel, Aug 04 2019

Sage

((1+x^8)/((1-x)*(1-x^2)*(1-x^3))).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Aug 04 2019

Formula

From Henry Bottomley, Sep 05 2000: (Start)

a(n) = floor((n^2 - 2*n + 18)/6) for n>2.

a(n) = a(n-2) + a(n-3) - a(n-5) + 2.

a(n) = A001399(n) + A001399(n-8).

a(n) = A008747(n-2) + 2 for n>2. (End)