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 A208208 a(n)=(a(n-1)^4*a(n-2)+1)/a(n-3) with a(0)=a(1)=a(2)=1. 3
 1, 1, 1, 2, 17, 167043, 6618080569762280805809 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS This is the case a=1, b=4, 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..8 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 = -0.588363990685104156421284586508527584304318862407786509166141051262... d2 = 0.4064206546327112651910488344937800073049991477253475806754539682375... d3 = 4.1819433360523928912302357520147475769993197146824389284906870830246... are the roots of the equation d^3 + 1 = 4*d^2 + d and c1 = 0.8094826741348488413005600397911253102639462301397489110738060562305... c2 = 0.5758908197062035276668941188013698534573120455706764136847247903030... c3 = 1.0094396347013780675988108222508397688561313671701492219003321772184... (End) MAPLE a:=proc(n) if n<3 then return 1: fi: return (a(n-1)^4*a(n-2)+1)/a(n-3): end: seq(a(i), i=0..10); MATHEMATICA RecurrenceTable[{a[n] == (a[n - 1]^4*a[n - 2] + 1)/a[n - 3], a[0] == a[1] == a[2] == 1}, a, {n, 0, 7}] (* Michael De Vlieger, Mar 19 2017 *) CROSSREFS Cf. A005246, A208207. Sequence in context: A269836 A114950 A112969 * A290189 A279883 A266166 Adjacent sequences:  A208205 A208206 A208207 * A208209 A208210 A208211 KEYWORD nonn AUTHOR Matthew C. Russell, Apr 23 2012 STATUS approved

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Last modified January 28 13:11 EST 2020. Contains 331321 sequences. (Running on oeis4.)