A208204 a(n) = (a(n-1)*a(n-2)^4+1)/a(n-3) with a(0)=a(1)=a(2)=1.

1, 1, 1, 2, 3, 49, 1985, 3814376662, 1208563686390770296199, 128885284912846137074628029815898112630258374651779168689

Offset

0,4

Comments

This is the case a=4, 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..12

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 = -1.699628148275317956229728291667145232598924547592878096541472700997...

d2 = 0.2391232782565544642500835033134825869161430421361867747730632704531...

d3 = 2.4605048700187634919796447883536626456827815054566913217684094305444...

are the roots of the equation d^3 + 1 = d^2 + 4*d and

c1 = 0.9668824482256124500532459849115781952211866063916062435395239896336...

c2 = 0.0680423294122660088493946488133224274885942757072304155092839505634...

c3 = 1.0386083844527725102069795872299989830277012965629707721463998933768...

(End)

Maple

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

Mathematica

a[0] = a[1] = a[2] = 1; a[n_] := a[n] = (a[n - 1]*a[n - 2]^4 + 1)/a[n - 3];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Dec 14 2017 *)

Crossrefs

Cf. A005246, A208203, A208205, A208211.

Sequence in context: A173355 A118222 A191594 * A067092 A041133 A113700

Adjacent sequences: A208201 A208202 A208203 * A208205 A208206 A208207

Keyword

nonn

Author

Matthew C. Russell, Apr 23 2012

Status

approved