A208227 a(n) = (a(n-1)^2*a(n-3)^4+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.

1, 1, 1, 1, 2, 5, 27, 11669, 42551737826, 192450770996317798484507077, 25433732883480327279167427243395261255488704554514737402263583619505

Offset: 0

Author

Matthew C. Russell, Apr 25 2012

Keywords

• nonn

Comments

This is the case a=4, 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).

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..12
• 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, A208224, A208226, A208228.

Programs

Maple

y:=proc(n) if n<4 then return 1: fi: return (y(n-1)^2*y(n-3)^4+y(n-2))/y(n-4): end:
seq(y(n),n=0..10);

Mathematica

a[n_]:=If[n<4,1, (a[n - 1]^2*a[n- 3]^4 + a[n - 2])/a[n - 4]]; Table[a[n], {n, 0, 10}] (* Indranil Ghosh, Mar 19 2017 *)