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%I #12 Sep 08 2022 08:45:32
%S -1,3,-1,2,-1,5,6,17,27,58,111,229,454,913,1819,3642,7279,14565,29126,
%T 58257,116507,233018,466031,932069,1864134,3728273,7456539,14913082,
%U 29826159,59652325,119304646,238609297,477218587,954437178,1908874351,3817748709,7635497414
%N a(n) = 3*A131090(n) - A131090(n+1).
%H G. C. Greubel, <a href="/A135261/b135261.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 A131090(n) - a(n) = A131556(n).
%F O.g.f.: (1-x)^2*(1-3*x)/((2*x-1)*(1+x)*(x^2-x+1)). - _R. J. Mathar_, Jul 22 2008
%F a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4). - _G. C. Greubel_, Oct 07 2016
%p seq(coeff(series((1-x)^2*(1-3*x)/((2*x-1)*(1+x)*(x^2-x+1)), x, n+1), x, n), n = 0 .. 40); # _G. C. Greubel_, Nov 21 2019
%t LinearRecurrence[{2,0,-1,2}, {-1,3,-1,2}, 40] (* _G. C. Greubel_, Oct 07 2016 *)
%o (PARI) my(x='x+O('x^40)); Vec((1-x)^2*(1-3*x)/((2*x-1)*(1+x)*(x^2-x+1))) \\ _G. C. Greubel_, Nov 21 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x)^2*(1-3*x)/((2*x-1)*(1+x)*(x^2-x+1)) )); // _G. C. Greubel_, Nov 21 2019
%o (Sage)
%o def A135261_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P((1-x)^2*(1-3*x)/((2*x-1)*(1+x)*(x^2-x+1))).list()
%o A135261_list(40) # _G. C. Greubel_, Nov 21 2019
%o (GAP) a:=[-1,2,-1,2];; for n in [5..40] do a[n]:=2*a[n-1] -a[n-3] +2*a[n-4]; od; a; # _G. C. Greubel_, Nov 21 2019
%K sign
%O 0,2
%A _Paul Curtz_, Dec 01 2007
%E Edited and extended by _R. J. Mathar_, Jul 22 2008
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