This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A027024 #18 Sep 08 2022 08:44:49
%S A027024 1,5,13,27,53,101,189,351,649,1197,2205,4059,7469,13741,25277,46495,
%T A027024 85521,157301,289325,532155,978789,1800277,3311229,6090303,11201817,
%U A027024 20603357,37895485,69700667,128199517,235795677,433695869
%N A027024 a(n) = T(n,n+2), T given by A027023.
%H A027024 G. C. Greubel, <a href="/A027024/b027024.txt">Table of n, a(n) for n = 2..1001</a>
%H A027024 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,-1).
%F A027024 G.f.: x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)).
%F A027024 a(n) = a(n-1) + a(n-2) + a(n-3) + 8, for n>4. - _Greg Dresden_, Feb 09 2020
%F A027024 a(n) = A000213(n+2)-4. - _R. J. Mathar_, Jun 24 2020
%p A027024 seq(coeff(series(x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)), x, n+1), x, n), n = 2..35); # _G. C. Greubel_, Nov 04 2019
%t A027024 Drop[CoefficientList[Series[x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)), {x, 0, 35}], x], 2] (* or *) LinearRecurrence[{2,0,0,-1}, {1,5,13,27}, 35] (* _G. C. Greubel_, Nov 04 2019 *)
%o A027024 (PARI) my(x='x+O('x^35)); Vec(x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3))) \\ _G. C. Greubel_, Nov 04 2019
%o A027024 (Magma) R<x>:=PowerSeriesRing(Integers(), 35); Coefficients(R!( x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)) )); // _G. C. Greubel_, Nov 04 2019
%o A027024 (Sage)
%o A027024 def A027024_list(prec):
%o A027024 P.<x> = PowerSeriesRing(ZZ, prec)
%o A027024 return P( x^2*(1+x)^3/((1-x)*(1-x-x^2-x^3)) ).list()
%o A027024 a=A027024_list(35); a[2:] # _G. C. Greubel_, Nov 04 2019
%o A027024 (GAP) a:=[1,5,13,27];; for n in [5..35] do a[n]:=2*a[n-1]-a[n-4]; od; a; # _G. C. Greubel_, Nov 04 2019
%Y A027024 Pairwise sums of A027053.
%K A027024 nonn,easy
%O A027024 2,2
%A A027024 _Clark Kimberling_