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A122100 a(n) = 3*a(n-1) - a(n-3) for n>2, with a(0)=1, a(1)=-1, a(2)=0.

%I A122100 #27 Sep 08 2022 08:45:28
%S A122100 1,-1,0,-1,-2,-6,-17,-49,-141,-406,-1169,-3366,-9692,-27907,-80355,
%T A122100 -231373,-666212,-1918281,-5523470,-15904198,-45794313,-131859469,
%U A122100 -379674209,-1093228314,-3147825473,-9063802210,-26098178316,-75146709475,-216376326215,-623030800329,-1793945691512
%N A122100 a(n) = 3*a(n-1) - a(n-3) for n>2, with a(0)=1, a(1)=-1, a(2)=0.
%H A122100 G. C. Greubel, <a href="/A122100/b122100.txt">Table of n, a(n) for n = 0..1000</a>
%H A122100 Paul Barry, <a href="https://arxiv.org/abs/2104.01644">Centered polygon numbers, heptagons and nonagons, and the Robbins numbers</a>, arXiv:2104.01644 [math.CO], 2021.
%H A122100 Kai Wang, <a href="https://www.researchgate.net/publication/337943524_Fibonacci_Numbers_And_Trigonometric_Functions_Outline">Fibonacci Numbers And Trigonometric Functions Outline</a>, (2019).
%H A122100 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-1).
%F A122100 G.f.: (1-4*x+3*x^2)/(1-3*x+x^3).
%p A122100 seq(coeff(series((1-4*x+3*x^2)/(1-3*x+x^3), x, n+1), x, n), n = 0 .. 40); # _G. C. Greubel_, Oct 02 2019
%t A122100 LinearRecurrence[{3,0,-1},{1,-1,0},40] (* _Harvey P. Dale_, Nov 14 2014 *)
%o A122100 (PARI) Vec((1-4*x+3*x^2)/(1-3*x+x^3)+O(x^40)) \\ _Charles R Greathouse IV_, Jan 17 2012
%o A122100 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-4*x+3*x^2)/(1-3*x+x^3) )); // _G. C. Greubel_, Oct 02 2019
%o A122100 (Sage)
%o A122100 def A122100_list(prec):
%o A122100     P.<x> = PowerSeriesRing(ZZ, prec)
%o A122100     return P((1-4*x+3*x^2)/(1-3*x+x^3)).list()
%o A122100 A122100_list(40) # _G. C. Greubel_, Oct 02 2019
%o A122100 (GAP) a:=[1,-1,0];; for n in [4..40] do a[n]:=3*a[n-1]-a[n-3]; od; a; # _G. C. Greubel_, Oct 02 2019
%Y A122100 Cf. A052536, A122099.
%K A122100 sign,easy,less
%O A122100 0,5
%A A122100 _Philippe Deléham_, Oct 18 2006