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 A208222 #15 May 31 2020 17:56:17
%S A208222 1,1,1,1,2,9,731,1562471573,154486807085783774292345385804
%N A208222 a(n) = (a(n-1)^3*a(n-3)^2+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.
%C A208222 This is the case a=2, b=1, c=3, y(0)=y(1)=y(2)=y(3)=1 of the recurrence shown in the Example 3.3 of "The Laurent phenomenon" (see Link lines, p. 10).
%H A208222 Seiichi Manyama, <a href="/A208222/b208222.txt">Table of n, a(n) for n = 0..11</a>
%H A208222 Sergey Fomin and Andrei Zelevinsky, <a href="http://arxiv.org/abs/math/0104241">The Laurent phenomenon</a>, arXiv:math/0104241v1 [math.CO] (2001), Advances in Applied Mathematics 28 (2002), 119-144.
%p A208222 y:=proc(n) if n<4 then return 1: fi: return (y(n-1)^3*y(n-3)^2+y(n-2))/y(n-4): end:
%p A208222 seq(y(n),n=0..9);
%t A208222 a[n_]:=If[n<4,1, (a[n - 1]^3*a[n - 3]^2 + a[n - 2])/a[n - 4]]; Table[a[n], {n, 0, 11}] (* _Indranil Ghosh_, Mar 19 2017 *)
%t A208222 nxt[{a_,b_,c_,d_}]:={b,c,d,(d^3 b^2+c)/a}; NestList[nxt,{1,1,1,1},10][[All,1]] (* _Harvey P. Dale_, May 31 2020 *)
%Y A208222 Cf. A048736, A208219, A208221, A208225.
%K A208222 nonn
%O A208222 0,5
%A A208222 _Matthew C. Russell_, Apr 25 2012