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A208218 a(n)=(a(n-1)^2*a(n-3)+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.

%I A208218 #14 Sep 08 2022 08:46:01
%S A208218 1,1,1,1,2,5,27,1463,5350936,154615586811211,
%T A208218 1295349936263652139582251464117,
%U A208218 6137049788665571444030885529267632764941063995324839557922175605
%N A208218 a(n)=(a(n-1)^2*a(n-3)+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.
%C A208218 This is the case a=1, b=1, c=2, 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 A208218 Seiichi Manyama, <a href="/A208218/b208218.txt">Table of n, a(n) for n = 0..14</a>
%H A208218 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 A208218 y:=proc(n) if n<4 then return 1: fi: return (y(n-1)^2*y(n-3)+y(n-2))/y(n-4): end:
%p A208218 seq(y(n),n=0..11);
%t A208218 RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==1,a[n]==(a[n-1]^2*a[n-3]+ a[n-2])/ a[n-4]},a,{n,12}] (* _Harvey P. Dale_, Dec 25 2016 *)
%o A208218 (Magma) [n le 4 select 1 else (Self(n-1)^2*Self(n-3)+Self(n-2))/Self(n-4): n in [1..12]]; // _Bruno Berselli_, Apr 24 2012
%Y A208218 Cf. A048736.
%K A208218 nonn
%O A208218 0,5
%A A208218 _Matthew C. Russell_, Apr 24 2012