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
Keywords
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.
Programs
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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);
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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 *)
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)
Comments