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A147605 Expansion of g.f.: 1/((1 - x^2 - x^3 - x^4 - x^5 - x^6 - x^7)*(1 + x + x^2 + x^3 + x^4 + x^5 - x^7)).

%I A147605 #17 Oct 25 2022 10:21:28
%S A147605 1,-1,1,0,1,1,3,3,3,10,11,21,32,52,77,128,206,320,517,817,1297,2060,
%T A147605 3290,5220,8298,13205,20980,33360,53056,84366,134114,213263,339086,
%U A147605 539123,857240,1363034,2167197,3445840,5478951,8711511,13851359
%N A147605 Expansion of g.f.: 1/((1 - x^2 - x^3 - x^4 - x^5 - x^6 - x^7)*(1 + x + x^2 + x^3 + x^4 + x^5 - x^7)).
%H A147605 G. C. Greubel, <a href="/A147605/b147605.txt">Table of n, a(n) for n = 0..1000</a>
%H A147605 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (-1,0,1,2,3,5,7,5,3,2,1,0,-1,-1).
%F A147605 G.f.: 1/(1 + x - x^3 - 2*x^4 - 3*x^5 - 5*x^6 - 7*x^7 - 5*x^8 - 3*x^9 - 2*x^10 - x^11 + x^13 + x^14).
%F A147605 G.f.: -1/(x^7*f(x)*f(1/x)), where f(x) = -1 + x^2 + x^3 + x^4 + x^5 + x^6 + x^7. - _G. C. Greubel_, Oct 24 2022
%t A147605 f[x_]= -1 +x^2 +x^3 +x^4 +x^5 +x^6 +x^7;
%t A147605 CoefficientList[Series[-1/(x^7*f[x]*f[1/x]), {x,0,50}], x] (* _G. C. Greubel_, Oct 24 2022 *)
%o A147605 (PARI) Vec(1/(1 +x -x^3 -2*x^4 -3*x^5 -5*x^6 -7*x^7 -5*x^8 -3*x^9 -2*x^10 -x^11 + x^13 +x^14) + O(x^40)) \\ _Jinyuan Wang_, Mar 10 2020
%o A147605 (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/((1-x^2-x^3-x^4-x^5-x^6-x^7)*(1+x+x^2+x^3+x^4+x^5-x^7)) )); // _G. C. Greubel_, Oct 24 2022
%o A147605 (SageMath)
%o A147605 def A147605_list(prec):
%o A147605     P.<x> = PowerSeriesRing(ZZ, prec)
%o A147605     return P( 1/((1-x^2-x^3-x^4-x^5-x^6-x^7)*(1+x+x^2+x^3+x^4+x^5-x^7)) ).list()
%o A147605 A147605_list(50) # _G. C. Greubel_, Oct 24 2022
%Y A147605 Cf. A107479, A147606, A147607, A147617.
%K A147605 sign,easy
%O A147605 0,7
%A A147605 _Roger L. Bagula_, Nov 08 2008
%E A147605 Definition corrected by _N. J. A. Sloane_, Nov 09 2008