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A112845
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Recurrence a[k]==a[k-1]^3-3a[k-1] with a[0]=6.
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4
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OFFSET
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0,1
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COMMENTS
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Identical to A006243 apart from the initial term. For some general remarks on this recurrence see A001999. - Peter Bala, Nov 13 2012
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REFERENCES
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E. B. Escott, Rapid method for extracting a square root, Amer. Math. Monthly, 44 (1937), 644-646.
N. J. Fine, Infinite products for k-th roots. Amer. Math. Monthly, Vol. 84, No. 8, Oct. 1977
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LINKS
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Table of n, a(n) for n=0..4.
Eric Weisstein's World of Mathematics, Pierce Expansion
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FORMULA
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-2*Cos[3^k*ArcCos[ -3]]
From Peter Bala, Nov 13 2012: (Start)
a(n) = (3 + 2*sqrt(2))^(3^n) + (3 - 2*sqrt(2))^(3^n).
Product {n = 0..inf} (1 + 2/(a(n) - 1)) = sqrt(2).
(End)
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CROSSREFS
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Cf. A006275, A006276.
Cf. A006243. [From R. J. Mathar, Aug 15 2008]. A001999, A219160, A219161.
Sequence in context: A156122 A086065 A200824 * A109058 A003743 A115491
Adjacent sequences: A112842 A112843 A112844 * A112846 A112847 A112848
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KEYWORD
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nonn,easy
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AUTHOR
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Eric W. Weisstein, Sep 21, 2005
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STATUS
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approved
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