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 A097122 #18 Jun 17 2024 22:48:13
%S A097122 1,1,1,4,13,31,70,169,421,1036,2521,6139,14998,36661,89545,218644,
%T A097122 533941,1304071,3184966,7778449,18996733,46394716,113307745,276726019,
%U A097122 675833686,1650553981,4031064961,9844867684,24043624093,58720529071
%N A097122 Expansion of (1-x)^2/((1-x)^3 - 3*x^3).
%D A097122 Maribel Díaz Noguera [Maribel Del Carmen Díaz Noguera], Rigoberto Flores, Jose L. Ramirez, and Martha Romero Rojas, Catalan identities for generalized Fibonacci polynomials, Fib. Q., 62:2 (2024), 100-111. See Table 3.
%H A097122 Seiichi Manyama, <a href="/A097122/b097122.txt">Table of n, a(n) for n = 0..1000</a>
%H A097122 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,4).
%F A097122 G.f.: (1-2*x+x^2)/(1-3*x+3*x^2-4*x^3).
%F A097122 a(n) = 3*a(n-1) - 3*a(n-2) + 4*a(n-3).
%F A097122 a(n) = Sum_{k=0..floor(n/3)} binomial(n, 3k) * 3^k.
%t A097122 CoefficientList[Series[(1-x)^2/((1-x)^3-3x^3),{x,0,40}],x]
%o A097122 (PARI) a(n) = sum(k=0, n\3, binomial(n, 3*k) * 3^k); \\ _Michel Marcus_, Oct 11 2021
%Y A097122 Cf. A024493, A052101, A100136.
%K A097122 easy,nonn
%O A097122 0,4
%A A097122 _Paul Barry_, Jul 25 2004