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 A099159 #26 Jun 21 2024 05:25:45
%S A099159 1,1,4,11,33,98,293,877,2628,7879,23629,70874,212601,637769,1913252,
%T A099159 5739667,17218857,51656338,154968637,464905301,1394714916,4184143151,
%U A099159 12552426869,37657276426,112971822513,338915456593,1016746352068,3050239027547,9150717036273
%N A099159 a(n) = (L(n-2)+2*3^n)/5.
%C A099159 Binomial transform of A052964.
%H A099159 Paolo Xausa, <a href="/A099159/b099159.txt">Table of n, a(n) for n = 0..1000</a>
%H A099159 Amya Luo, <a href="https://math.dartmouth.edu/theses/undergrad/2024/Luo-thesis.pdf">Pattern Avoidance in Nonnesting Permutations</a>, Undergraduate Thesis, Dartmouth College (2024). See p. 16.
%H A099159 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-3).
%F A099159 G.f.: (1-3*x+2*x^2)/((1-3*x)*(1-x-x^2)).
%F A099159 a(n) = ((1+sqrt(5))/2)^n*(3/10-sqrt(5)/10) + ((1-sqrt(5))/2)^n*(3/10+sqrt(5)/10) + 3^n*2/5.
%F A099159 a(n) = Sum_{k=0..n} (-2*0^k-Fib(k-4)) * 3^(n-k).
%F A099159 a(n) = A098703(n+1) - A098703(n). - _Ross La Haye_, Sep 11 2005
%t A099159 A099159[n_] := (LucasL[n-2] + 2*3^n)/5; Array[A099159, 30, 0] (* or *)
%t A099159 LinearRecurrence[{4, -2, -3}, {1, 1, 4}, 30] (* _Paolo Xausa_, Jun 20 2024 *)
%Y A099159 Cf. A000032, A052964, A098703, A101220,
%K A099159 easy,nonn
%O A099159 0,3
%A A099159 _Paul Barry_, Oct 01 2004