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Search: id:A072879
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| A072879 |
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a(n)=5*a(n-1)*a(n-2)*a(n-3)*a(n-4) - a(n-5). |
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+0
4
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| 1, 1, 1, 1, 1, 4, 19, 379, 144019, 20741616379, 107553662508585672001, 608831069421618273050865038881215685876, 978035016076705458999330010986670207956236476587064788804921180339451725001
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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Solutions of the Hurwitz equation in five variables.
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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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FORMULA
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a(1)=a(2)=a(3)=a(4)=a(5)=1; a(n)=(a(n-1)^2+a(n-2)^2+a(n-3)^2+a(n-4)^2)/a(n-5).
From the recurrence a(n)=5*a(n-1)*a(n-2)*a(n-3)*a(n-4) - a(n-5), any five successive terms satisfy the five-variable Hurwitz equation a(n)^2+a(n-1)^2+a(n-2)^2+a(n-3)^2+a(n-4)^2=5*a(n)*a(n-1)*a(n-2)*a(n-3)*a(n-4), As n tends to infinity, the limit of log(log(a(n)))/n is log x = 0.6562559790... where x=1.927561975... is the largest real root of the quartic x^4-x^3-x^2-x-1=0. - Andrew Hone (anwh(AT)kent.ac.uk), Nov 16 2005
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CROSSREFS
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Cf. A006720, A072878.
Sequence in context: A155804 A126147 A007411 this_sequence A112958 A080991 A000844
Adjacent sequences: A072876 A072877 A072878 this_sequence A072880 A072881 A072882
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), 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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