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 A099560 #17 Dec 08 2022 11:36:50
%S A099560 0,0,0,1,1,1,3,4,5,9,13,18,28,41,59,88,129,188,277,406,594,872,1278,
%T A099560 1872,2745,4023,5895,8641,12664,18559,27201,39865,58424,85626,125491,
%U A099560 183915,269542,395033,578948,848491,1243524,1822472,2670964,3914488
%N A099560 a(n) = Sum_{k=0..floor(n/3)} C(n-2k,k-1).
%H A099560 G. C. Greubel, <a href="/A099560/b099560.txt">Table of n, a(n) for n = 0..1000</a>
%H A099560 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-1,0,-1).
%F A099560 G.f.: x^3/((1-x^3)(1-x-x^3)).
%F A099560 a(n) = a(n-1) + 2*a(n-3) - a(n-4) - a(n-6).
%F A099560 a(n) = a(n-3) + A000930(n-3). - _R. J. Mathar_, Nov 24 2013
%F A099560 a(n) = A000930(n-2) - A079978(n+1), n>3. - _R. J. Mathar_, Dec 08 2022
%t A099560 Table[Sum[Binomial[n-2k,k-1],{k,0,Floor[n/3]}],{n,0,50}] (* or *) LinearRecurrence[{1,0,2,-1,0,-1},{0,0,0,1,1,1},50] (* _Harvey P. Dale_, May 25 2014 *)
%t A099560 CoefficientList[Series[x^3/((1 - x^3) (1 - x - x^3)), {x,0,50}], x] (* _G. C. Greubel_, Apr 28 2017 *)
%o A099560 (PARI) x='x+O('x^50); concat([0,0,0], Vec(x^3/((1-x^3)*(1-x-x^3)))) \\ _G. C. Greubel_, Apr 28 2017
%Y A099560 Cf. A074331, A099561, A099562.
%K A099560 easy,nonn
%O A099560 0,7
%A A099560 _Paul Barry_, Oct 22 2004