OFFSET
0,4
COMMENTS
This is the case a=2, b=2, y(0)=y(1)=y(2)=1 of the recurrence shown in the Example 3.2 of "The Laurent phenomenon" (see Link lines, p. 10).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..11
Joshua Alman, Cesar Cuenca, and Jiaoyang Huang, Laurent phenomenon sequences, Journal of Algebraic Combinatorics 43(3) (2015), 589-633.
Sergey Fomin and Andrei Zelevinsky, The Laurent phenomenon, arXiv:math/0104241v1 [math.CO] (2001); Advances in Applied Mathematics 28 (2002), 119-144.
FORMULA
From Vaclav Kotesovec, May 20 2015: (Start)
a(n) ~ c1^(d1^n) * c2^(d2^n) * c3^(d3^n), where
d1 = -1
d2 = (3-sqrt(5))/2 = 0.381966011250105151795413165634361882279690820194237...
d3 = (3+sqrt(5))/2 = 2.618033988749894848204586834365638117720309179805762...
are the roots of the equation d^3 + 1 = 2*d^2 + 2*d and
c1 = 0.9084730936822995591913406002175634029260903950386034752117808169903...
c2 = 0.3198114201427769362008537317523839726550617444688426214134486371587...
c3 = 1.0375048945851318188473394167711806349224412339663566324740449820203...
(End)
MAPLE
a:=proc(n) if n<3 then return 1: fi: return (a(n-1)^2*a(n-2)^2+1)/a(n-3): end: seq(a(i), i=0..10);
MATHEMATICA
a[0] = a[1] = a[2] = 1; a[n_] := a[n] = (a[n-1]^2*a[n-2]^2 + 1)/a[n-3];
Table[a[n], {n, 0, 11}] (* Jean-François Alcover, Nov 17 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Matthew C. Russell, Apr 23 2012
STATUS
approved