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Search: id:A086594
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| A086594 |
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a(n)=8a(n-1)+a(n-2), starting with a(0)=2 and a(1)=8. |
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+0
3
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| 2, 8, 66, 536, 4354, 35368, 287298, 2333752, 18957314, 153992264, 1250895426, 10161155672, 82540140802, 670482282088, 5446398397506, 44241669462136, 359379754094594, 2919279702218888
(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, build on the number 8.1231056...
a(n+1)/a(n) converges to 4+sqrt(17). a(0)/a(1)=1/4; a(1)/a(2)=8/66; a(2)/a(3)=66/536; a(3)/a(4)=536/4354;...etc. Lim a(n)/a(n+1)as n approaches infinity=0.123105625...=1/(4+sqrt(17))=sqrt(17)-4.
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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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a(n)=(4+sqrt(17))^n+(4-sqrt(17))^n.
O.g.f: 2*(-1+4*x)/(-1+8*x+x^2) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 02 2007
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EXAMPLE
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a(4)=4354=8a(3)+a(2)=8*536+66=(4+sqrt(17))^4+(4-sqrt(17))^4=4353.9997703+
0.0002297=4354.
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CROSSREFS
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Cf. A003285.
Sequence in context: A009602 A011836 A100623 this_sequence A132219 A023164 A053922
Adjacent sequences: A086591 A086592 A086593 this_sequence A086595 A086596 A086597
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KEYWORD
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easy,nonn
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AUTHOR
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Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Sep 11 2003
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