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%I #13 Sep 08 2022 08:45:32
%S 0,-1,2,1,3,2,7,13,30,57,115,226,455,909,1822,3641,7283,14562,29127,
%T 58253,116510,233017,466035,932066,1864135,3728269,7456542,14913081,
%U 29826163,59652322,119304647,238609293,477218590,954437177,1908874355,3817748706
%N a(n) = 3*A131666(n) - A131666(n+1).
%H G. C. Greubel, <a href="/A135259/b135259.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 (2,0,-1,2).
%F A131666(n) - a(n) = A092220(n).
%F O.g.f.: x*(1-x)*(1 -3*x)/( (2*x-1)*(x+1)*(1 -x +x^2) ). - _R. J. Mathar_, Jul 22 2008
%F a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4). - _G. C. Greubel_, Oct 05 2016
%p seq(coeff(series(x*(1-x)*(1-3*x)/((2*x-1)*(x+1)*(1-x+x^2)), x, n+1), x, n), n = 0 .. 35); # _G. C. Greubel_, Nov 21 2019
%t LinearRecurrence[{2,0,-1,2}, {0,-1,2,1}, 35] (* _G. C. Greubel_, Oct 05 2016 *)
%o (PARI) concat(0, Vec(x*(1-x)*(1-3*x)/((2*x-1)*(x+1)*(1-x+x^2)) + O(x^35))) \\ _Michel Marcus_, Oct 05 2016
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 35); [0] cat Coefficients(R!( x*(1-x)*(1-3*x)/((2*x-1)*(x+1)*(1-x+x^2)) )); // _G. C. Greubel_, Nov 21 2019
%o (Sage)
%o def A135259_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P(x*(1-x)*(1-3*x)/((2*x-1)*(x+1)*(1-x+x^2))).list()
%o A135259_list(35) # _G. C. Greubel_, Nov 21 2019
%o (GAP) a:=[0,-1,2,1];; for n in [5..35] do a[n]:=2*a[n-1]-a[n-3]+2*a[n-4]; od; a; # _G. C. Greubel_, Nov 21 2019
%Y Cf. A131666.
%K sign
%O 0,3
%A _Paul Curtz_, Dec 01 2007
%E Edited and extended by _R. J. Mathar_, Jul 22 2008
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