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%I #21 Sep 08 2022 08:45:48
%S 1,1,-1,-3,-3,-5,-7,-7,-9,-11,-11,-13,-15,-15,-17,-19,-19,-21,-23,-23,
%T -25,-27,-27,-29,-31,-31,-33,-35,-35,-37,-39,-39,-41,-43,-43,-45,-47,
%U -47,-49,-51,-51,-53,-55,-55,-57,-59,-59,-61,-63,-63,-65,-67,-67,-69
%N Expansion of (1-2*x^2-3*x^3)/((1-x)^2*(1+x+x^2)).
%H G. C. Greubel, <a href="/A168053/b168053.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F a(n) = -(n^9 -45n^8 +846n^7 -8610n^6 +51345n^5 -181125n^4 +361584n^3 -361260n^2 +137264n -6720)/6720.
%F a(n) = A168054(n)/2^n.
%t LinearRecurrence[{1,0,1,-1},{1,1,-1,-3},60] (* _Harvey P. Dale_, Jan 15 2015 *)
%t CoefficientList[Series[(1 - 2 x^2 - 3 x^3) / ((1 - x)^2 (1 + x + x^2)), {x, 0, 80}], x] (* _Vincenzo Librandi_, Jul 08 2016 *)
%o (Magma) m:=55; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-2*x^2-3*x^3)/((1-x)^2*(1+x+x^2)))); // _Bruno Berselli_, May 31 2013
%Y Cf. A168054.
%K sign,easy
%O 0,4
%A _Paul Barry_, Nov 17 2009
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