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A147620 Expansion of g.f.: 1/((1 - x - x^2 + x^6 - x^8)*(1 - x^2 + x^6 + x^7 - x^8)).

%I A147620 #10 Oct 24 2022 15:12:56
%S A147620 1,1,3,4,8,12,19,29,46,70,111,170,271,422,668,1048,1655,2603,4104,
%T A147620 6453,10167,15989,25175,39599,62329,98064,154335,242845,382183,601399,
%U A147620 946451,1489366,2343847,3688412,5804459,9134287,14374533,22620800,35597998
%N A147620 Expansion of g.f.: 1/((1 - x - x^2 + x^6 - x^8)*(1 - x^2 + x^6 + x^7 - x^8)).
%H A147620 G. C. Greubel, <a href="/A147620/b147620.txt">Table of n, a(n) for n = 0..1000</a>
%H A147620 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-1,-1,0,-2,0,5,0,-2,0,-1,-1,2,1,-1).
%F A147620 G.f.: 1/(1 - x - 2*x^2 + x^3 + x^4 + 2*x^6 - 5*x^8 + 2*x^10 + x^12 + x^13 - 2*x^14 - x^15 + x^16).
%t A147620 f[x_]= -1+x^2-x^6-x^7+x^8;
%t A147620 CoefficientList[Series[-1/(x^8*f[x]*f[1/x]), {x, 0, 50}], x]
%o A147620 (PARI) Vec(1/(1-x-2*x^2+x^3+x^4+2*x^6-5*x^8+2*x^10+x^12+x^13-2*x^14-x^15+x^16) + O(x^40)) \\ _Jinyuan Wang_, Mar 10 2020
%o A147620 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1-x-x^2+x^6- x^8)*(1-x^2+x^6+x^7-x^8)) )); // _G. C. Greubel_, Oct 24 2022
%o A147620 (SageMath)
%o A147620 def A147620_list(prec):
%o A147620     P.<x> = PowerSeriesRing(ZZ, prec)
%o A147620     return P( 1/((1-x-x^2+x^6-x^8)*(1-x^2+x^6+x^7-x^8)) ).list()
%o A147620 A147620_list(40) # _G. C. Greubel_, Oct 24 2022
%Y A147620 Cf. A147607, A147617, A147621.
%K A147620 nonn
%O A147620 0,3
%A A147620 _Roger L. Bagula_, Nov 08 2008
%E A147620 Definition corrected by _N. J. A. Sloane_, Nov 09 2008