A008678 Expansion of 1/((1-x^3)*(1-x^5)*(1-x^7)*(1-x^9)).

1, 0, 0, 1, 0, 1, 1, 1, 1, 2, 2, 1, 3, 2, 3, 4, 3, 4, 5, 5, 5, 7, 6, 7, 9, 8, 9, 11, 11, 11, 14, 13, 14, 17, 16, 18, 20, 20, 21, 24, 24, 25, 29, 28, 30, 34, 33, 35, 39, 39, 41, 45, 45, 47, 52, 52, 54, 59, 59, 62, 67, 67

Offset

0,10

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 238

Index entries for linear recurrences with constant coefficients, signature (0, 0, 1, 0, 1, 0, 1, -1, 1, -1, 0, -2, 0, -1, 1, -1, 1, 0, 1, 0, 1, 0, 0, -1).

Maple

seq(coeff(series(1/mul(1-x^(2*j+1), j=1..4), x, n+1), x, n), n = 0..70); # G. C. Greubel, Sep 09 2019

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^5)(1-x^7)(1-x^9)), {x, 0, 70}], x] (* Harvey P. Dale, Sep 30 2011 *)

Prog

(PARI) my(x='x+O('x^70)); Vec(1/prod(j=1, 4, 1-x^(2*j+1))) \\ G. C. Greubel, Sep 09 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/&*[1-x^(2*j+1): j in [1..4]] )); // G. C. Greubel, Sep 09 2019
(Sage)
def A008678_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/prod(1-x^(2*j+1) for j in (1..4)) ).list()
A008678_list(70) # G. C. Greubel, Sep 09 2019

Crossrefs

Sequence in context: A319444 A071285 A289438 * A159803 A308934 A058741

Adjacent sequences: A008675 A008676 A008677 * A008679 A008680 A008681

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved