A122767 Expansion of 2*x/(1-6*x-120*x^2+300*x^3).

0, 2, 12, 312, 2712, 50112, 532512, 8394912, 99237312, 1443059712, 18048362112, 251686144512, 3243002406912, 44245843149312, 579129504371712, 7811377482074112, 103090052472256512, 1382166761370918912

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, Sep 22 2006

Keywords

• nonn
• easy
• less

Links

• G. C. Greubel, Table of n, a(n) for n = 0..875
• P. Steinbach, Golden fields: a case for the heptagon, Math. Mag. 70 (1997), no. 1, 22-31.
• Index entries for linear recurrences with constant coefficients, signature (6,120,-300).

Crossrefs

Cf. A078008, A122601.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30); [0] cat Coefficients(R!( 2*x/(1-6*x-120*x^2+300*x^3) )); // G. C. Greubel, Dec 31 2022

Mathematica

CoefficientList[Series[2x/(1-6x-120x^2+300x^3),{x,0,20}],x] (* or *) LinearRecurrence[{6,120,-300},{0,2,12},20] (* Harvey P. Dale, Oct 16 2016 *)

PARI

Vec(2*x/(1-6*x-120*x^2+300*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

SageMath

def A122767_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 2*x/(1-6*x-120*x^2+300*x^3) ).list()
A122767_list(30) # G. C. Greubel, Dec 31 2022