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Search: id:A087798
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| A087798 |
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a(n) = 9a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 9, a(n) = [(9+sqrt(85))/2]^n + [(9-sqrt(85))/2]^n. |
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| 2, 9, 83, 756, 6887, 62739, 571538, 5206581, 47430767, 432083484, 3936182123, 35857722591, 326655685442, 2975758891569, 27108485709563, 246952130277636, 2249677658208287, 20494051054152219, 186696137145578258
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Harmonious sequence, built on the number 9.10977...
a(n+1)/a(n) converges to (9+sqrt(85))/2 = 9.10977... a(0)/a(1)=2/9; a(1)/a(2)=9/83; a(2)/a(3)=83/756; a(3)/a(4)=756/6887; ... etc. Lim a(n)/a(n+1) as n approaches infinity = 0.1097722... = 2/(9+sqrt(85)) = (sqrt(85)-9)/2.
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LINKS
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Tanya Khovanova, Recursive Sequences
Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)
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FORMULA
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G.f.: (2-9*x)/(1-9*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 02 2008]
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EXAMPLE
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a(4) = 6887 = 9a(3) + a(2) = 9*756 + 83 = [(9+sqrt(85))/2]^4 + [(9-sqrt(85))/2]^4 = 6886.9998547 + 0.0001452 = 6887.
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CROSSREFS
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Cf. A014511.
Sequence in context: A123570 A006040 A067309 this_sequence A113146 A069234 A086929
Adjacent sequences: A087795 A087796 A087797 this_sequence A087799 A087800 A087801
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KEYWORD
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easy,nonn
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AUTHOR
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Nikolay V. Kosinov, Dmitry V. Poljakov (kosinov(AT)unitron.com.ua), Oct 10 2003
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EXTENSIONS
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More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 06 2003
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