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A075298 Inverted (definition in A075193) generalized tribonacci numbers A001644.

%I A075298 #26 Sep 08 2022 08:45:07
%S A075298 1,1,-5,5,1,-11,15,-3,-23,41,-21,-43,105,-83,-65,253,-271,-47,571,
%T A075298 -795,177,1189,-2161,1149,2201,-5511,4459,3253,-13223,14429,2047,
%U A075298 -29699,42081,-10335,-61445,113861,-62751,-112555,289167,-239363,-162359,690889,-767893,-85355,1544137,-2226675,597183,3173629
%N A075298 Inverted (definition in A075193) generalized tribonacci numbers A001644.
%C A075298 a(n) = -C(n+1), C(n)=reflected generalized tribonacci numbers A073145.
%H A075298 G. C. Greubel, <a href="/A075298/b075298.txt">Table of n, a(n) for n = 0..5000</a>
%H A075298 Curtis Cooper, S. Miller, Peter J. C. Moses, M. Sahin, and T. Thanatipanonda, <a href="http://thotsaporn.com/Cooper.pdf">On Identities of Ruggles, Horadam, Howard, and Young</a>, Preprint 2016.
%H A075298 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,1).
%F A075298 a(n) = -a(n-1) - a(n-2) + a(n-3), a(0)=1, a(1)=1, a(2)=-5.
%F A075298 G.f.: (1+2*x-3*x^2)/(1+x+x^2-x^3).
%F A075298 a(n) = A078046(n) + 3*A078046(n-1). - _R. J. Mathar_, Sep 20 2020
%t A075298 CoefficientList[Series[(1+2x-3x^2)/(1+x+x^2-x^3), {x, 0, 50}], x]
%o A075298 (PARI) my(x='x+O('x^50)); Vec((1+2*x-3*x^2)/(1+x+x^2-x^3)) \\ _G. C. Greubel_, Apr 09 2019
%o A075298 (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+2*x-3*x^2)/(1+x+x^2-x^3) )); // _G. C. Greubel_, Apr 09 2019
%o A075298 (Sage) ((1+2*x-3*x^2)/(1+x+x^2-x^3)).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 09 2019
%o A075298 (GAP) a:=[1,1,-5];; for n in [4..50] do a[n]:=-a[n-1]-a[n-2]+a[n-3]; od; a; # _G. C. Greubel_, Apr 09 2019
%Y A075298 Cf. A001644, A073145, A075193.
%K A075298 easy,sign
%O A075298 0,3
%A A075298 Mario Catalani (mario.catalani(AT)unito.it), Sep 13 2002