Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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