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A208223 a(n) = (a(n-1)*a(n-3)^3+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.

%I A208223 #18 Mar 17 2023 07:12:52
%S A208223 1,1,1,1,2,3,5,43,583,24306,386499545,1781091354996947,
%T A208223 43869039083107828857967559,
%U A208223 104205727286975116465887590166696643681426291537,1523355234093129576841463666274426784578547247551635338205747270819704358703763325458
%N A208223 a(n) = (a(n-1)*a(n-3)^3+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.
%C A208223 This is the case a=3, b=1, c=1, 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 A208223 Seiichi Manyama, <a href="/A208223/b208223.txt">Table of n, a(n) for n = 0..18</a>
%H A208223 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 A208223 y:=proc(n) if n<4 then return 1: fi: return (y(n-1)*y(n-3)^3+y(n-2))/y(n-4): end:
%p A208223 seq(y(n),n=0..14);
%t A208223 RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==1,a[n]==(a[n-1]a[n-3]^3+a[n-2])/ a[n-4]},a,{n,20}] (* _Harvey P. Dale_, Jul 13 2014 *)
%o A208223 (Magma) [n le 4 select 1 else (Self(n-1)*Self(n-3)^3+Self(n-2))/Self(n-4): n in [1..15]]; // _Bruno Berselli_, Apr 26 2012
%Y A208223 Cf. A048736.
%K A208223 nonn
%O A208223 0,5
%A A208223 _Matthew C. Russell_, Apr 25 2012