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%I #28 Sep 08 2022 08:45:08
%S 1,-1,-1,4,-3,-6,16,-7,-31,61,-6,-147,220,68,-655,739,639,-2772,2233,
%T 3950,-11188,5521,20805,-43035,6946,99929,-156856,-36056,449697,
%U -534441,-401009,1919588,-1652011,-2588174,7811784,-4287447,-13924295,30310973,-6749830,-67796411,111607044,17235948
%N Expansion of 1/(1+x+2*x^2-x^3).
%H G. C. Greubel, <a href="/A077978/b077978.txt">Table of n, a(n) for n = 0..1000</a>
%H Yüksel Soykan, <a href="https://arxiv.org/abs/1910.03490">Summing Formulas For Generalized Tribonacci Numbers</a>, arXiv:1910.03490 [math.GM], 2019.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-2,1).
%F a(n) = (-1)^n * A077955(n). - _G. C. Greubel_, Jun 25 2019
%t LinearRecurrence[{-1,-2,1}, {1,-1,-1}, 50] (* or *) CoefficientList[ Series[1/(1+x+2*x^2-x^3), {x, 0, 50}], x] (* _G. C. Greubel_, Jun 25 2019 *)
%o (PARI) Vec(1/(1+x+2*x^2-x^3)+O(x^50)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1+x+2*x^2-x^3) )); // _G. C. Greubel_, Jun 25 2019
%o (Sage) (1/(1+x+2*x^2-x^3)).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 25 2019
%o (GAP) a:=[1,-1,-1];; for n in [4..50] do a[n]:=-a[n-1]-2*a[n-2]+a[n-3]; od; a; # _G. C. Greubel_, Jun 25 2019
%Y Cf. A077955, A077911, A078049.
%K sign,easy
%O 0,4
%A _N. J. A. Sloane_, Nov 17 2002
%E Deleted certain dangerous or potentially dangerous links. - _N. J. A. Sloane_, Jan 30 2021
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