A008719 Expansion of 1/((1-x)*(1-x^4)*(1-x^6)*(1-x^12)).

1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 8, 8, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 27, 27, 30, 30, 36, 36, 42, 42, 48, 48, 54, 54, 64, 64, 70, 70, 80, 80, 90, 90, 100, 100, 110, 110, 125, 125, 135, 135, 150, 150, 165, 165, 180, 180, 195, 195, 216, 216, 231, 231, 252, 252, 273, 273, 294

Offset

0,5

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 242

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

Maple

seq(coeff(series(1/((1-x)*(1-x^4)*(1-x^6)*(1-x^12)), x, n+1), x, n), n = 0..70); # G. C. Greubel, Sep 09 2019

Mathematica

CoefficientList[Series[1/((1-x)(1-x^4)(1-x^6)(1-x^12)), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 23 2013 *)
LinearRecurrence[{1, 0, 0, 1, -1, 1, -1, 0, 0, -1, 1, 1, -1, 0, 0, -1, 1, -1, 1, 0, 0, 1, -1}, {1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 8, 8, 9, 9, 12, 12, 15, 15, 18, 18, 21}, 80] (* Harvey P. Dale, Apr 03 2022 *)

Prog

(PARI) my(x='x+O('x^70)); Vec(1/((1-x)*(1-x^4)*(1-x^6)*(1-x^12))) \\ G. C. Greubel, Sep 09 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/((1-x)*(1-x^4)*(1-x^6)*(1-x^12)) )); // G. C. Greubel, Sep 09 2019
(Sage)
def A008719_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P(1/((1-x)*(1-x^4)*(1-x^6)*(1-x^12))).list()
A008719_list(70) # G. C. Greubel, Sep 09 2019

Crossrefs

Sequence in context: A227614 A236473 A029030 * A079685 A112409 A256991

Adjacent sequences: A008716 A008717 A008718 * A008720 A008721 A008722

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Typo in name fixed by Vincenzo Librandi, Jun 23 2013

Status

approved