A069950 Expansion of (1+x^2)*(1+x^5)*(1+x^8)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)*(1-x^7)*(1-x^8)*(1-x^9)*(1-x^10)).

1, 1, 3, 4, 7, 11, 17, 25, 38, 53, 77, 105, 146, 196, 265, 350, 462, 600, 778, 994, 1270, 1601, 2016, 2514, 3126, 3857, 4745, 5797, 7063, 8554, 10331, 12411, 14871, 17734, 21093, 24986, 29519, 34747, 40801, 47746, 55746, 64884, 75353

Offset: 0

Author

N. J. A. Sloane, May 05 2002

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• G. E. Andrews, P. Paule and A. Riese, MacMahon's Partition Analysis VIII: Plane partition diamonds, Advances Applied Math., 27 (2001), 231-242.
• Index entries for linear recurrences with constant coefficients, signature (1, 2, -1, -2, 1, 1, -3, -1, 3, 1, -3, 2, 4, -1, -2, 1, -1, -3, -1, 0, 0, 0, 2, 2, 2, 0, 0, 0, -1, -3, -1, 1, -2, -1, 4, 2, -3, 1, 3, -1, -3, 1, 1, -2, -1, 2, 1, -1).

Crossrefs

Cf. A008763, A060962.

Programs

Magma

R:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^2)*(1+x^5)*(1+x^8)/( (&*[1-x^j: j in [1..10]]) ) )); // G. C. Greubel, Aug 16 2022

Mathematica

CoefficientList[Series[(1+x^2)*(1+x^5)*(1+x^8)/(1-x)/(1-x^2)/(1-x^3)/(1-x^4)/ (1-x^5)/(1-x^6)/(1-x^7)/(1-x^8)/(1-x^9)/(1-x^10),{x,0,60}],x] (* Harvey P. Dale, Feb 25 2013 *)

PARI

Vec((1+x^2)*(1+x^5)*(1+x^8)/(1-x)/(1-x^2)/(1-x^3)/(1-x^4)/(1-x^5)/(1-x^6)/(1-x^7)/(1-x^8)/(1-x^9)/(1-x^10)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

Sage

def A069950_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x^2)*(1+x^5)*(1+x^8)/product(1-x^j for j in (1..10)) ).list()
A069950_list(60) # G. C. Greubel, Aug 16 2022

Formula

G.f.: (1+x^2)*(1+x^5)*(1+x^8)/( Product_{j=1..10} (1-x^j) ). - G. C. Greubel, Aug 16 2022