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%I #14 Oct 25 2022 01:35:54
%S 1,1,3,4,8,10,17,24,37,55,85,132,202,317,488,761,1171,1818,2802,4333,
%T 6688,10334,15964,24661,38115,58886,91011,140619,217317,335783,518882,
%U 801765,1238908,1914362,2958086,4570887,7062966,10913848,16864199
%N Expansion of g.f.: 1/((1 - x - x^2 + x^5 - x^7)*(1 - x^2 + x^5 + x^6 - x^7)).
%H G. C. Greubel, <a href="/A147617/b147617.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-1,-1,-2,0,5,0,-2,-1,-1,2,1,-1).
%F G.f.: 1/(1 - x - 2*x^2 + x^3 + x^4 + 2*x^5 - 5*x^7 + 2*x^9 + x^10 + x^11 - 2*x^12 - x^13 + x^14).
%F G.f.: -1/(x^7*f(x)*f(1/x)), where f(x) = -1 + x + x^2 - x^5 + x^7. - _G. C. Greubel_, Oct 24 2022
%t f[x_]= -1+x+x^2-x^5+x^7;
%t CoefficientList[Series[-1/(x^7*f[x]*f[1/x]), {x, 0, 50}], x] (* _G. C. Greubel_, Oct 24 2022 *)
%o (PARI) Vec(1/(1 -x -2*x^2 +x^3 +x^4 +2*x^5 -5*x^7 +2*x^9 +x^10 +x^11 -2*x^12 - x^13 +x^14) + O(x^40)) \\ _Jinyuan Wang_, Mar 10 2020
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1-x-x^2+x^5- x^7)*(1-x^2+x^5+x^6-x^7)) )); // _G. C. Greubel_, Oct 24 2022
%o (SageMath)
%o def A147617_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( 1/((1-x-x^2+x^5-x^7)*(1-x^2+x^5+x^6-x^7)) ).list()
%o A147617_list(40) # _G. C. Greubel_, Oct 24 2022
%Y Cf. A147607, A147620, A147621.
%K nonn,easy,less
%O 0,3
%A _Roger L. Bagula_, Nov 08 2008
%E Definition corrected by _N. J. A. Sloane_, Nov 09 2008
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