A124314 - OEIS

%I #16 Aug 26 2023 02:53:17

%S -1,1,0,0,0,-2,3,-1,0,0,-4,8,-5,1,0,-8,20,-18,7,-1,-16,48,-56,32,-9,

%T -31,112,-160,120,-50,-53,255,-432,400,-220,-56,563,-1119,1232,-840,

%U 108,1182,-2801,3583,-2912,1056,2256,-6784,9967,-9407,5024

%N Expansion of -1/(1 + x + x^2 + x^3 + x^4 - x^5).

%H G. C. Greubel, <a href="/A124314/b124314.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,-1,-1,1).

%t CoefficientList[Series[1/(-1-x-x^2-x^3-x^4+x^5), {x,0,50}], x]

%t LinearRecurrence[{-1,-1,-1,-1,1}, {-1,1,0,0,0}, 60] (* _G. C. Greubel_, Aug 25 2023 *)

%o (PARI) Vec(1/(-1-x-x^2-x^3-x^4+x^5)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (-1+x)/(1-2*x^5+x^6) )); // _G. C. Greubel_, Aug 25 2023

%o (SageMath)

%o def A124314_list(prec):

%o     P.<x> = PowerSeriesRing(ZZ, prec)

%o     return P( (-1+x)/(1-2*x^5+x^6) ).list()

%o A124314_list(60) # _G. C. Greubel_, Aug 25 2023

%Y Cf. A124312, A124313.

%K sign,easy

%O 0,6

%A _Artur Jasinski_, Oct 25 2006