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Expansion of -1/(1 - x + 3*x^2 - 2*x^3 + x^4 - 2*x^5 + x^6).
2

%I #17 Sep 28 2024 07:36:53

%S -1,-1,2,3,-4,-10,5,29,2,-76,-45,178,212,-361,-750,565,2282,-306,

%T -6206,-2428,15176,14353,-32719,-55104,57933,176234,-61524,-499047,

%U -97429,1271400,921652,-2887641,-3948938,5590078,13380187,-7828378,-39536779,108416,104810904

%N Expansion of -1/(1 - x + 3*x^2 - 2*x^3 + x^4 - 2*x^5 + x^6).

%H G. C. Greubel, <a href="/A129920/b129920.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,-3,2,-1,2,-1).

%F a(n) = a(n-1) - 3*a(n-2) + 2*a(n-3) - a(n-4) + 2*a(n-5) - a(n-6), n >= 6. - _Franck Maminirina Ramaharo_, Jan 08 2019

%t CoefficientList[Series[-1/(1-x +3*x^2 -2*x^3 +x^4 -2*x^5 +x^6), {x,0,50}], x]

%o (Magma)

%o R<x>:=PowerSeriesRing(Integers(), 50);

%o Coefficients(R!( -1/(1-x+3*x^2-2*x^3+x^4-2*x^5+x^6) )); // _G. C. Greubel_, Sep 28 2024

%o (SageMath)

%o def A129920_list(prec):

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

%o return P( -1/(1-x+3*x^2-2*x^3+x^4-2*x^5+x^6) ).list()

%o A129920_list(50) # _G. C. Greubel_, Sep 28 2024

%Y Cf. A008620, A010892, A014019, A099443, A099479, A099480, A112712.

%Y Cf. A125629, A129704, A129903.

%K sign,easy

%O 0,3

%A _Roger L. Bagula_, Jun 05 2007

%E Edited by _Franck Maminirina Ramaharo_, Jan 08 2019