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%I #18 Oct 31 2024 18:50:25
%S 1,2,3,8,18,42,97,225,521,1207,2796,6477,15004,34757,80515,186514,
%T 432062,1000877,2318544,5370936,12441840,28821677,66765773,154663743,
%U 358280483,829961192,1922615417,4453762510,10317196211,23899913257,55364446116,128252427562,297098342519,688232003132
%N Expansion of (x^4+x^3+x^2-x-1)/(x^4+2*x^3+2*x^2+x-1).
%D Based on a suggestion of _Wolfdieter Lang_ in A272362.
%H Vincenzo Librandi, <a href="/A272642/b272642.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,0,-1,-1).
%F G.f.: (x^4+x^3+x^2-x-1)/(x^4+2*x^3+2*x^2+x-1).
%F a(n) = 2*a(n-1) + a(n-2) - a(n-4) - a(n-5). - _Vincenzo Librandi_, May 08 2016
%t CoefficientList[Series[(x^4 + x^3 + x^2 - x - 1)/(x^4 + 2 x^3 + 2 x^2 + x - 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, May 08 2016 *)
%t LinearRecurrence[{1,2,2,1},{1,2,3,8,18},40] (* _Harvey P. Dale_, Oct 31 2024 *)
%o (Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((x^4+x^3+x^2-x-1)/(x^4+2*x^3+2*x^2+x-1))); // _Bruno Berselli_, May 08 2016
%Y A272362 gives partial sums.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, May 07 2016