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A147593 Expansion of 1/(1 - x + x^3 - 3*x^4 + x^5 - x^7 + x^8).

%I A147593 #12 Oct 26 2022 03:05:07
%S A147593 1,1,1,0,2,3,5,3,6,8,16,16,24,28,50,61,91,109,170,220,327,415,607,800,
%T A147593 1164,1536,2192,2928,4172,5616,7921,10705,15049,20460,28638,39027,
%U A147593 54453,74451,103662,141996,197288,270704,375632,516096,715258,983661,1362091
%N A147593 Expansion of 1/(1 - x + x^3 - 3*x^4 + x^5 - x^7 + x^8).
%H A147593 G. C. Greubel, <a href="/A147593/b147593.txt">Table of n, a(n) for n = 0..1000</a>
%H A147593 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,-1,3,-1,0,1,-1).
%F A147593 G.f.: -1/(x^4*f(x)*f(1/x)), where f(x) = -1 - x^3 + x^4.
%F A147593 G.f.: 1/((1+x^3-x^4)*(1-x-x^4)). - _Colin Barker_, Nov 04 2012
%t A147593 f[x_]= x^4-x^3-1; CoefficientList[Series[-1/(x^4*f[x]*f[1/x]), {x,0,50}], x]
%o A147593 (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/((1+x^3-x^4)*(1-x-x^4)) )); // _G. C. Greubel_, Oct 25 2022
%o A147593 (SageMath)
%o A147593 def A147593_list(prec):
%o A147593     P.<x> = PowerSeriesRing(ZZ, prec)
%o A147593     return P( 1/((1+x^3-x^4)*(1-x-x^4)) ).list()
%o A147593 A147593_list(50) # _G. C. Greubel_, Oct 25 2022
%Y A147593 Cf. A147598, A147605, A147606, A147607, A147617, A147620.
%K A147593 nonn,easy
%O A147593 0,5
%A A147593 _Roger L. Bagula_, Nov 08 2008
%E A147593 Edited by _Joerg Arndt_ and _Colin Barker_, Nov 04 2012.