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 A121253 #15 Sep 08 2022 08:45:27
%S A121253 0,0,0,1,1,1,2,3,4,9,28,113,1018,28505,3221066,3279045189,
%T A121253 93469183112446,301070407771273987437,987223472152664180906141290594,
%U A121253 92274971491542102812339702600558728264132925
%N A121253 a(n) = a(n-1)*a(n-3)+1 with a(0)=a(1)=a(2)=0.
%C A121253 Analog of A007660 a(n)=a(n-1)*a(n-2)+1. What is the equivalent continued fraction and asymptotic representation?
%H A121253 Vincenzo Librandi, <a href="/A121253/b121253.txt">Table of n, a(n) for n = 0..26</a> (shortened by _N. J. A. Sloane_, Jan 13 2019)
%t A121253 RecurrenceTable[{a[0]==a[1]==a[2]==0,a[n]==a[n-1]a[n-3]+1},a,{n,20}] (* _Harvey P. Dale_, Dec 30 2011 *)
%o A121253 (Magma) I:=[0,0,0]; [n le 3 select I[n] else Self(n-1)*Self(n-3)+1: n in [1..20]]; // _Vincenzo Librandi_, Nov 14 2011
%Y A121253 Cf. A007660.
%K A121253 nonn,easy
%O A121253 0,7
%A A121253 _Jonathan Vos Post_, Aug 22 2006
%E A121253 More terms from _Vincenzo Librandi_, Nov 14 2011