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A147598 Expansion of g.f. 1/((1-x^2+x^3+x^4-x^5)*(1-x-x^2+x^3-x^5)).

%I A147598 #8 Oct 25 2022 20:06:50
%S A147598 1,1,3,2,4,3,6,9,14,23,29,45,57,88,123,184,267,382,556,787,1149,1643,
%T A147598 2392,3444,4978,7184,10348,14956,21550,31152,44924,64881,93611,135101,
%U A147598 195000,281382,406201,586164,846121,1221064,1762399,2543555,3671003
%N A147598 Expansion of g.f. 1/((1-x^2+x^3+x^4-x^5)*(1-x-x^2+x^3-x^5)).
%H A147598 G. C. Greubel, <a href="/A147598/b147598.txt">Table of n, a(n) for n = 0..1000</a>
%H A147598 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-3,-1,5,-1,-3,2,1,-1).
%F A147598 G.f.: -1/(x^5*f(x)*f(1/x)), where f(x) = -1 +x^2 -x^3 -x^4 +x^5.
%F A147598 G.f.: 1/((x^5-x^4-x^3+x^2-1)*(x^5-x^3+x^2+x-1)). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009
%t A147598 f[x_]= x^5 -x^4 -x^3 +x^2 -1;
%t A147598 CoefficientList[Series[-1/(x^5*f[x]*f[1/x]), {x,0,50}],x]
%o A147598 (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/((1-x^2+x^3+x^4-x^5)*(1-x-x^2+x^3-x^5)) )); // _G. C. Greubel_, Oct 25 2022
%o A147598 (SageMath)
%o A147598 def A147598_list(prec):
%o A147598     P.<x> = PowerSeriesRing(ZZ, prec)
%o A147598     return P( 1/((1-x^2+x^3+x^4-x^5)*(1-x-x^2+x^3-x^5)) ).list()
%o A147598 A147598_list(50) # _G. C. Greubel_, Oct 25 2022
%Y A147598 Cf. A147605, A147606, A147607, A147617, A147620.
%K A147598 nonn,easy,less
%O A147598 0,3
%A A147598 _Roger L. Bagula_, Nov 08 2008
%E A147598 Better name (using g.f.) from _Joerg Arndt_, Apr 06 2018