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A147606 Expansion of g.f.: 1/((1 - x - x^2 + x^4 - x^6)*(1 - x^2 + x^4 + x^5 - x^6)).

%I A147606 #11 Oct 25 2022 20:07:10
%S A147606 1,1,3,4,6,8,12,15,25,35,56,84,130,192,294,432,654,972,1466,2192,3308,
%T A147606 4953,7463,11185,16820,25224,37906,56868,85445,128239,192643,289196,
%U A147606 434364,652124,979372,1470436,2208192,3315556,4978892,7475948,11226252
%N A147606 Expansion of g.f.: 1/((1 - x - x^2 + x^4 - x^6)*(1 - x^2 + x^4 + x^5 - x^6)).
%H A147606 G. C. Greubel, <a href="/A147606/b147606.txt">Table of n, a(n) for n = 0..1000</a>
%H A147606 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-1,-3,0,5,0,-3,-1,2,1,-1).
%F A147606 G.f.: 1/(1 - x - 2*x^2 + x^3 + 3*x^4 - 5*x^6 + 3*x^8 + x^9 - 2*x^10 - x^11 + x^12).
%F A147606 G.f.: -1/(x^6*f(x)*f(1/x)), where f(x) = -1 + x + x^2 - x^4 + x^6. - _G. C. Greubel_, Oct 24 2022
%t A147606 f[x_]= -1+x+x^2-x^4+x^6;
%t A147606 CoefficientList[Series[-1/(x^6*f[x]*f[1/x]), {x, 0, 50}], x] (* _G. C. Greubel_, Oct 24 2022 *)
%o A147606 (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/((1-x-x^2+x^4-x^6)*(1-x^2+x^4+x^5-x^6)) )); // _G. C. Greubel_, Oct 24 2022
%o A147606 (SageMath)
%o A147606 def A147606_list(prec):
%o A147606     P.<x> = PowerSeriesRing(ZZ, prec)
%o A147606     return P( 1/((1-x-x^2+x^4-x^6)*(1-x^2+x^4+x^5-x^6)) ).list()
%o A147606 A147606_list(50) # _G. C. Greubel_, Oct 24 2022
%Y A147606 Cf. A109537, A147607, A147617.
%K A147606 nonn,easy
%O A147606 0,3
%A A147606 _Roger L. Bagula_, Nov 08 2008
%E A147606 Definition corrected by _N. J. A. Sloane_, Nov 09 2008