A208211 a(n)=(a(n-1)^2*a(n-2)^4+1)/a(n-3) with a(0)=a(1)=a(2)=1.

1, 1, 1, 2, 5, 401, 50250313, 13058251494934169005517674, 2711319949800838662068317571116321157238013748056632969662193456875554487084437

Offset

0,4

Comments

This is the case a=4, 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).

The next term, a(9), has 250 digits. - Harvey P. Dale, May 12 2015

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10

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 = -1.391382380630900845100729034616031832171938259539254240563846155543...

d2 = 0.2271344421706896320468868758105588761186297860618178147525916240716...

d3 = 3.1642479384602112130538421588054729560533084734774364258112545314714...

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

c1 = 0.9492747639156309053009206968548726546571223067568220073025225799006...

c2 = 0.2025736158012536053359109009272747757676200151893348144191432397054...

c3 = 1.0182066570849459786725527422494583474915007718333213073686225606760...

(End)

Maple

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

Mathematica

RecurrenceTable[{a[0]==a[1]==a[2]==1, a[n]==(a[n-1]^2*a[n-2]^4+1)/a[n-3]}, a, {n, 9}] (* Harvey P. Dale, May 12 2015 *)

Crossrefs

Cf. A005246, A208204, A208210, A208212.

Sequence in context: A183129 A081462 A035128 * A138696 A163798 A081296

Adjacent sequences: A208208 A208209 A208210 * A208212 A208213 A208214

Keyword

nonn

Author

Matthew C. Russell, Apr 23 2012

Status

approved