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%I #20 Jul 08 2022 12:01:15
%S 1,-3,6,-13,29,-64,141,-311,686,-1513,3337,-7360,16233,-35803,78966,
%T -174165,384133,-847232,1868629,-4121391,9090014,-20048657,44218705,
%U -97527424,215103505,-474425715,1046378854,-2307861213,5090148141,-11226675136,24761211485,-54612571111,120451817358
%N Expansion of (1-x)/(1+2*x+x^3).
%H Shanzhen Gao, Keh-Hsun Chen, <a href="http://worldcomp-proceedings.com/proc/p2014/FCS2696.pdf">Tackling Sequences From Prudent Self-Avoiding Walks</a>, FCS'14, The 2014 International Conference on Foundations of Computer Science.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-2,0,-1).
%F a(n) = (-1)^n*sum{k=0..n, C(n-k,floor(k/2))*2^(n-k-floor(k/2))}. [_Paul Barry_, Oct 20 2009]
%F (-1)^n*a(n) = A008998(n)+A008998(n-1). - _R. J. Mathar_, Jul 08 2022
%t CoefficientList[Series[(1-x)/(1+2x+x^3),{x,0,40}],x] (* or *) LinearRecurrence[ {-2,0,-1},{1,-3,6},40] (* _Harvey P. Dale_, Dec 15 2017 *)
%o (PARI) Vec((1-x)/(1+2*x+x^3)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 27 2012
%K sign,easy
%O 0,2
%A _N. J. A. Sloane_, Nov 17 2002
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