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%I #9 Oct 27 2018 11:00:47
%S 1,0,-1,1,0,-2,2,1,-4,3,3,-8,4,8,-15,4,19,-27,0,42,-46,-15,88,-73,-57,
%T 176,-104,-160,337,-120,-393,617,-64,-890,1074,209,-1900,1755,1035,
%U -3864,2620,3144,-7519,3340,8043,-14003,2816,18706,-24862,-1887,40752,-41681,-17777,84320,-64656,-60416,166753,-88560,-162513
%N Expansion of 1/(1+x^2-x^3+x^4).
%C Expansion of the characteristic polynomial of Jones polynomial for the Solomon knot (L4a1): f(x)=-1/Sqrt[x] + 1/x^{3/2} - 1/x^{5/2} - 1/x^{9/2};
%H Knot atlas, <a href="http://katlas.org/wiki/L4a1">L4a1</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,-1,1,-1).
%t f[q_] = -1/Sqrt[q] + 1/q^{3/2} - 1/q^{5/2} - 1/q^{9/2} FullSimplify[ExpandAll[f[q]/Sqrt[q]]]; g[q_] = 1 + q^2 - q^3 + q^4; q[x_] := 1/g[x]; Table[ SeriesCoefficient[Series[q[x], {x, 0, 30}], n], {n, 0, 30}]
%t LinearRecurrence[{0,-1,1,-1},{1,0,-1,1},70] (* _Harvey P. Dale_, Oct 27 2018 *)
%K easy,sign
%O 0,6
%A _Roger L. Bagula_, Jun 04 2007
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