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A208220 a(n)=(a(n-1)*a(n-3)^2+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1. 2

%I #17 Sep 08 2022 08:46:01

%S 1,1,1,1,2,3,5,23,106,891,94289,46062265,344980727309,

%T 3442224480935856594,77458438596193694601268422031,

%U 200130424073190804359006946314196714242380417,6873796333354760314538446350412794888765818679762438117097006307173727

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

%C This is the case a=2, 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 Seiichi Manyama, <a href="/A208220/b208220.txt">Table of n, a(n) for n = 0..21</a>

%H 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 y:=proc(n) if n<4 then return 1: fi: return (y(n-1)*y(n-3)^2+y(n-2))/y(n-4): end:

%p seq(y(n),n=0..16);

%t a[n_] := a[n] = (a[n - 1]*a[n - 3]^2 + a[n - 2])/a[n - 4];

%t a[0] = a[1] = a[2] = a[3] = 1;

%t Table[a[n], {n, 0, 16}] (* _Jean-Fran├žois Alcover_, Apr 01 2018 *)

%o (Magma) [n le 4 select 1 else (Self(n-1)*Self(n-3)^2+Self(n-2))/Self(n-4): n in [1..17]]; // Bruno Berselli, Apr 26 2012

%Y Cf. A048736.

%K nonn

%O 0,5

%A _Matthew C. Russell_, Apr 25 2012

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