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A208203 a(n) = (a(n-1)*a(n-2)^3+1)/a(n-3) with a(0)=a(1)=a(2)=1. 4
1, 1, 1, 2, 3, 25, 338, 1760417, 2719102918193, 43888992061611808973481301345, 501206842313618355048837897498360450999462416742984495192498 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

This is the case a=3, b=1, 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..13

Sergey Fomin and Andrei Zelevinsky, The Laurent phenomenon, arXiv:math/0104241v1 [math.CO] (2001).

Sergey Fomin and Andrei Zelevinsky, The Laurent phenomenon, 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 = -1.481194304092015622633537241216857180552745216998476728395893140813...

d2 = 0.3111078174659818999302814767914862551326055871751667747271657344269...

d3 = 2.1700864866260337227032557644253709254201396298233099536687274063868...

are the roots of the equation d^3 + 1 = d^2 + 3*d and

c1 = 0.9558632550121524723294926402589664329208850973886195977958538648966...

c2 = 0.0925177857987965285678801091508493414479538300221910521000975614673...

c3 = 1.0621981744880569938247885786471114069804924018378928906529142898259...

(End)

MAPLE

a:=proc(n) if n<3 then return 1: fi: return (a(n-1)*a(n-2)^3+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]*a[n - 2]^3 + 1)/a[n - 3];

Table[a[n], {n, 0, 13}] (* Jean-Fran├žois Alcover, Dec 14 2017 *)

CROSSREFS

Cf. A005246, A208202, A208204, A208210.

Sequence in context: A296281 A226018 A094998 * A109586 A060371 A130975

Adjacent sequences:  A208200 A208201 A208202 * A208204 A208205 A208206

KEYWORD

nonn

AUTHOR

Matthew C. Russell, Apr 23 2012

STATUS

approved

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Last modified July 14 16:05 EDT 2020. Contains 335729 sequences. (Running on oeis4.)