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 A027975 #16 Sep 08 2022 08:44:49
%S A027975 1,1,4,5,8,12,16,23,31,42,57,76,102,136,181,241,320,425,564,748,992,
%T A027975 1315,1743,2310,3061,4056,5374,7120,9433,12497,16556,21933,29056,
%U A027975 38492,50992,67551,89487,118546,157041,208036,275590,365080,483629,640673,848712,1124305,1489388,1973020
%N A027975 a(n) is the n-th diagonal sum of left justified array T given by A027960.
%H A027975 G. C. Greubel, <a href="/A027975/b027975.txt">Table of n, a(n) for n = 0..1000</a>
%H A027975 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1).
%F A027975 G.f.: (1 + 2*x^2)/((1-x)*(1-x^2-x^3)).
%F A027975 a(n) = a(n-2) + a(n-3) + 3. - _Greg Dresden_, May 18 2020
%p A027975 seq(coeff(series((1+2*x^2)/((1-x)*(1-x^2-x^3)), x, n+1), x, n), n = 0..40); # _G. C. Greubel_, Sep 26 2019
%t A027975 CoefficientList[Series[(1+2*x^2)/((1-x)*(1-x^2-x^3)), {x,0,40}], x] (* or *) LinearRecurrence[{1,1,0,-1}, {1,1,4,5}, 41] (* _G. C. Greubel_, Sep 26 2019 *)
%o A027975 (PARI) my(x='x+O('x^40)); Vec((1+2*x^2)/((1-x)*(1-x^2-x^3))) \\ _G. C. Greubel_, Sep 26 2019
%o A027975 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+2*x^2)/((1-x)*(1-x^2-x^3)) )); // _G. C. Greubel_, Sep 26 2019
%o A027975 (Sage)
%o A027975 def A027975_list(prec):
%o A027975 P.<x> = PowerSeriesRing(ZZ, prec)
%o A027975 return P( (1+2*x^2)/((1-x)*(1-x^2-x^3)) ).list()
%o A027975 A027975_list(40) # _G. C. Greubel_, Sep 26 2019
%o A027975 (GAP) a:=[1,1,4,5];; for n in [5..40] do a[n]:=a[n-1]+a[n-2]-a[n-4]; od; a; # _G. C. Greubel_, Sep 26 2019
%Y A027975 Cf. A027960.
%K A027975 nonn
%O A027975 0,3
%A A027975 _Clark Kimberling_
%E A027975 Terms a(32) onward added by _G. C. Greubel_, Sep 26 2019