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.

1, 1, 1, 1, 2, 3, 5, 23, 106, 891, 94289, 46062265, 344980727309, 3442224480935856594, 77458438596193694601268422031, 200130424073190804359006946314196714242380417, 6873796333354760314538446350412794888765818679762438117097006307173727

Offset: 0

Author

Matthew C. Russell, Apr 25 2012

Keywords

• nonn
• changed

Comments

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).

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..21
• Sergey Fomin and Andrei Zelevinsky, The Laurent phenomenon, arXiv:math/0104241v1 [math.CO] (2001), Advances in Applied Mathematics 28 (2002), 119-144.

Crossrefs

Cf. A048736.

Programs

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

Maple

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:
seq(y(n),n=0..16);

Mathematica

a[n_] := a[n] = (a[n - 1]*a[n - 3]^2 + a[n - 2])/a[n - 4];
a[0] = a[1] = a[2] = a[3] = 1;
Table[a[n], {n, 0, 16}] (* Jean-François Alcover, Apr 01 2018 *)