A175714 Expansion of -1/((1 - x)*(1 - x^2 + 4*x^3)).

-1, -1, -2, 2, 1, 9, -8, 4, -45, 35, -62, 214, -203, 461, -1060, 1272, -2905, 5511, -7994, 17130, -30039, 49105, -98560, 169260, -294981, 563499, -972022, 1743422, -3226019, 5631509, -10199708, 18535584, -32725745, 59334415, -106868082, 190237394, -344205743, 617709721

Offset

0,3

Comments

The ratio a(n+1)/a(n) approaches -1.7963219032594415... as n-> infinity.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-5,4).

Formula

G.f.: -1/((1 - x)*(1 - x^2 + 4*x^3)).

Maple

seq(coeff(series(-1/((1-x)*(1-x^2+4*x^3)), x, n+1), x, n), n = 0..40); # G. C. Greubel, Dec 04 2019

Mathematica

LinearRecurrence[{1, 1, -5, 4}, {-1, -1, -2, 2}, 40] (* Bruno Berselli, May 17 2017 *)

Prog

(PARI) my(x='x+O('x^40)); Vec(-1/((1-x)*(1-x^2+4*x^3))) \\ G. C. Greubel, Dec 04 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( -1/((1-x)*(1-x^2+4*x^3)) )); // G. C. Greubel, Dec 04 2019
(Sage)
def A175714_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( -1/((1-x)*(1-x^2+4*x^3)) ).list()
A175714_list(40) # G. C. Greubel, Dec 04 2019
(GAP) a:=[-1, -1, -2, 2];; for n in [5..40] do a[n]:=a[n-1]+a[n-2]-5*a[n-3] + 4*a[n-4]; od; a; # G. C. Greubel, Dec 04 2019

Crossrefs

Sequence in context: A126586 A128463 A136730 * A291082 A295855 A364371

Adjacent sequences: A175711 A175712 A175713 * A175715 A175716 A175717

Keyword

sign,easy

Author

Roger L. Bagula, Dec 04 2010

Status

approved