login
A175714
Expansion of -1/((1 - x)*(1 - x^2 + 4*x^3)).
1
-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.
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
KEYWORD
sign,easy
AUTHOR
Roger L. Bagula, Dec 04 2010
STATUS
approved