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 A122299 #28 Mar 11 2025 13:51:17
%S A122299 0,1,1,5,12,38,107,316,915,2671,7771,22640,65922,191993,559112,
%T A122299 1628281,4741905,13809541,40216516,117119750,341079507,993301748,
%U A122299 2892722267,8424270271,24533405595,71446899736,208069745986,605946785585,1764655909392,5139082429553
%N A122299 Expansion of x * (1-x) / ( 1 - 2*x - 3*x^2 + x^3 ).
%C A122299 Essentially the same as A095310. - _Georg Fischer_, Oct 07 2018
%H A122299 Muniru A Asiru, <a href="/A122299/b122299.txt">Table of n, a(n) for n = 1..500</a>
%H A122299 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-1)
%F A122299 a(n)= +2*a(n-1) +3*a(n-2) -a(n-3).
%p A122299 seq(coeff(series(x*(1-x)/(1-2*x-3*x^2+x^3),x,n+1), x, n), n = 0 .. 30); # _Muniru A Asiru_, Oct 07 2018
%t A122299 CoefficientList[Series[x*(1-x)/(1-2*x-3*x^2+x^3), {x,0,30}], x] (* _G. C. Greubel_, Oct 08 2018 *)
%t A122299 LinearRecurrence[{2,3,-1},{0,1,1},40] (* _Harvey P. Dale_, Mar 11 2025 *)
%o A122299 (GAP) a:=[0,1,1];; for n in [4..30] do a[n]:=2*a[n-1]+3*a[n-2]-a[n-3]; od; a; # _Muniru A Asiru_, Oct 07 2018
%o A122299 (Magma) I:=[0,1,1]; [n le 3 select I[n] else 2*Self(n-1)+3*Self(n-2)-Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Oct 08 2018
%o A122299 (PARI) x='x+O('x^30); concat([0], Vec(x*(1-x)/(1-2*x-3*x^2+x^3))) \\ _G. C. Greubel_, Oct 08 2018
%K A122299 nonn
%O A122299 1,4
%A A122299 _Gary W. Adamson_ and _Roger L. Bagula_, Oct 19 2006