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A208209 a(n) = (a(n-1)^2*a(n-2)^2 + 1)/a(n-3) with a(0)=a(1)=a(2)=1. 7
1, 1, 1, 2, 5, 101, 127513, 33172764857794, 177153971843949087009428690473769185 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A066618 A027720 A132482 * A276267 A215845 A276110
KEYWORD
nonn
AUTHOR
Matthew C. Russell, Apr 23 2012
STATUS
approved

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Last modified February 24 10:50 EST 2024. Contains 370295 sequences. (Running on oeis4.)