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 A099213 #16 Aug 31 2022 09:10:37 %S A099213 1,1,1,5,9,17,41,85,177,385,817,1733,3705,7889,16793,35797,76257, %T A099213 162433,346081,737285,1570665,3346193,7128713,15186901,32354193, %U A099213 68927233,146842129,312831941,666455769,1419814097,3024765689,6443947093 %N A099213 a(n) = a(n-1)+a(n-2)+3a(n-3), with a(0)=a(1)=a(2)=1. %C A099213 Binomial transform is A099214. Binomial transform of A099212. %H A099213 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,3). %F A099213 G.f.: (1-x^2)/(1-x-x^2-3*x^3). [corrected by _Michel Marcus_, Aug 31 2022] %o A099213 (Sage) from sage.combinat.sloane_functions import recur_gen3; it = recur_gen3(1,1,1,1,1,3); [next(it) for i in range(32)] # _Zerinvary Lajos_, Jun 25 2008 %o A099213 (PARI) Vec((1-x^2)/(1-x-x^2-3*x^3) + O(x^30)) \\ _Michel Marcus_, Aug 31 2022 %Y A099213 Cf. A099212, A099214. %K A099213 easy,nonn %O A099213 0,4 %A A099213 _Paul Barry_, Oct 06 2004