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%I #22 Sep 08 2022 08:46:09
%S 1,0,0,0,-1,1,0,0,1,-2,1,0,-1,3,-3,1,1,-4,6,-4,0,5,-10,10,-4,-5,15,
%T -20,14,1,-20,35,-34,13,21,-55,69,-47,-8,76,-124,116,-39,-84,200,-240,
%U 155,45,-284,440,-395,110,329,-724,835,-505,-219,1053,-1559,1340
%N Expansion of 1 / (1 + x^4 - x^5) in powers of x.
%H Vincenzo Librandi, <a href="/A247919/b247919.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 (0,0,0,-1,1).
%F G.f.: 1 / ((1 - x + x^2) * (1 + x - x^3)).
%F Convolution of A010892 and A247917.
%F a(-5-n) = A003520(n) for all n in Z.
%F 0 = a(n) - a(n+1) - a(n+5) for all n in Z.
%e G.f. = 1 - x^4 + x^5 + x^8 - 2*x^9 + x^10 - x^12 + 3*x^13 - 3*x^14 + x^15 + ...
%t CoefficientList[Series[1/(1 + x^4 - x^5), {x, 0, 100}], x] (* _Vincenzo Librandi_, Sep 27 2014 *)
%o (PARI) {a(n) = if( n<0, n=-5-n; polcoeff( 1 / (1 - x - x^5) + x * O(x^n), n), polcoeff( 1 / (1 + x^4 - x^5) + x * O(x^n), n))};
%o (Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1 + x^4 - x^5))); // _G. C. Greubel_, Aug 04 2018
%Y Cf. A003520, A010892, A247917.
%K sign,easy
%O 0,10
%A _Michael Somos_, Sep 26 2014
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