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 A128214 #17 Jul 16 2021 14:28:38
%S A128214 1,0,0,-2,3,0,-5,6,0,-8,9,0,-11,12,0,-14,15,0,-17,18,0,-20,21,0,-23,
%T A128214 24,0,-26,27,0,-29,30,0,-32,33,0,-35,36,0,-38,39,0,-41,42,0,-44,45,0,
%U A128214 -47,48,0,-50,51,0,-53,54,0,-56,57,0,-59,60,0,-62,63,0,-65
%N A128214 Expansion of (1+2x+3x^2)/(1+x+x^2)^2.
%C A128214 Binomial transform is A128213.
%H A128214 Harvey P. Dale, <a href="/A128214/b128214.txt">Table of n, a(n) for n = 0..1000</a>
%H A128214 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-2,-3,-2,-1).
%F A128214 G.f.: (1+2x+3x^2)/(1+x+x^2)^2.
%F A128214 a(n) = (1-n)*cos(2*Pi*n/3)+(n-1)*sin(2*Pi*n/3)/sqrt(3).
%F A128214 a(n) = (-1)^n*( A099254(n)-2*A099254(n-1)+3*A099254(n-2) ). - _R. J. Mathar_, Mar 21 2011
%F A128214 From _Wesley Ivan Hurt_, Mar 15 2015: (Start)
%F A128214 a(n) + 2*a(n-1) + 3*a(n-2) + 2*a(n-3) + a(n-4) = 0.
%F A128214 a(n) = (n-1) * ((n-2)^2 mod 3) * (-1)^floor((2n-2)/3). (End)
%t A128214 CoefficientList[Series[(1 + 2 x + 3 x^2)/(1 + x + x^2)^2, {x, 0, 50}], x] (* _Wesley Ivan Hurt_, Mar 15 2015 *)
%t A128214 LinearRecurrence[{-2,-3,-2,-1},{1,0,0,-2},70] (* _Harvey P. Dale_, Jul 16 2021 *)
%o A128214 (PARI) Vec((1+2*x+3*x^2)/(1+x+x^2)^2 + O(x^80)) \\ _Michel Marcus_, Mar 16 2015
%Y A128214 Cf. A128213.
%K A128214 easy,sign
%O A128214 0,4
%A A128214 _Paul Barry_, Feb 19 2007
%E A128214 More terms from _Wesley Ivan Hurt_, Mar 15 2015