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A072878
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a(n)=4*a(n-1)*a(n-2)*a(n-3) - a(n-4).
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5
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1, 1, 1, 1, 3, 11, 131, 17291, 99665321, 903016046275353, 6224717403288400029624460201, 2240882930472585840954332388399544581477407095086361
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OFFSET
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1,5
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COMMENTS
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A subsequence of the generalized Markoff numbers.
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REFERENCES
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A. Baragar, Integral solutions of the Markoff-Hurwitz equations, J. Number Theory 49 (1994) 27-44.
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LINKS
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Table of n, a(n) for n=1..12.
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FORMULA
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a(1)=a(2)=a(3)=a(4)=1; a(n)=(a(n-1)^2+a(n-3)^2+a(n-2)^2)/a(n-4).
From the recurrence a(n)=4*a(n-1)*a(n-2)*a(n-3) - a(n-4), any four successive terms satisfy the Markoff-Hurwitz equation a(n)^2+a(n-1)^2+a(n-2)^2+a(n-3)^2=4*a(n)*a(n-1)*a(n-2)*a(n-3), cf. A075276. As n tends to infinity, the limit of log(log(a(n)))/n is log x = 0.6093778633... where x=1.839286755... is the real root of the cubic x^3-x^2-x-1=0. - Andrew Hone (anwh(AT)kent.ac.uk), Nov 14 2005
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CROSSREFS
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Cf. A075276, A072879.
Sequence in context: A201611 A088075 A088076 * A112957 A057205 A121897
Adjacent sequences: A072875 A072876 A072877 * A072879 A072880 A072881
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre, Jul 28 2002
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EXTENSIONS
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Entry revised Nov 19, 2005, based on comments from Andrew Hone (anwh(AT)kent.ac.uk)
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STATUS
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approved
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