A008682 Expansion of 1/((1-x^4)*(1-x^5)*(1-x^6)).

1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 2, 1, 2, 2, 3, 2, 3, 2, 4, 3, 4, 3, 5, 4, 5, 4, 6, 5, 7, 5, 7, 6, 8, 7, 9, 7, 9, 8, 11, 9, 11, 9, 12, 11, 13, 11, 14, 12, 15, 13, 16, 14, 17, 15, 18, 16, 19, 17, 21, 18, 21, 19, 23, 21, 24, 21, 25, 23, 27, 24, 28, 25, 29, 27, 31, 28, 32, 29, 34, 31

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 229
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,1,1,0,0,-1,-1,-1,0,0,0,1).

Programs

Magma

R:=PowerSeriesRing(Integers(), 90); Coefficients(R!( 1/&*[1-x^j: j in [4..6]] )); // G. C. Greubel, Sep 09 2019

Maple

seq(coeff(series(1/mul(1-x^j, j=4..6), x, n+1), x, n), n = 0..90); # G. C. Greubel, Sep 09 2019

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^5)(1-x^6)), {x,0,90}], x] (* Vincenzo Librandi, Jun 23 2013 *)

PARI

Vec(1/(1-x^4)*(1-x^5)*(1-x^6)+O(x^90)) \\ Charles R Greathouse IV, Sep 26 2012

Sage

def A008682_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P(1/prod(1-x^j for j in (4..6))).list()
A008682_list(90) # G. C. Greubel, Sep 09 2019

Extensions

Typo in name fixed by Vincenzo Librandi, Jun 23 2013

More terms added from b-file. - G. C. Greubel, Sep 09 2019