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Search: id:A089772
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| 2, 199, 39603, 7881196, 1568397607, 312119004989, 62113250390418, 12360848946698171, 2459871053643326447, 489526700523968661124, 97418273275323406890123, 19386725908489881939795601
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OFFSET
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0,1
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COMMENT
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a(n+1)/a(n) converges to (199+sqrt(39605))/2 = 199.00502499874... a(0)/a(1)=2/199; a(1)/a(2)=199/39603; a(2)/a(3)= 39603/7881196; a(3)/a(4)= 7881196/1568397607; ... etc. Lim a(n)/a(n+1) as n approaches infinity = 0.00502499874... = 2/(199+sqrt(39605)) = (sqrt(39605)-199)/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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a(n) =199a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 199 a(n) = ((199+sqrt(39605))/2)^n +((199-sqrt(39605))/2)^n, (a(n))^2 =a(2n)-2 if n=1, 3, 5..., (a(n))^2 =a(2n)+2 if n=2, 4, 6....
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EXAMPLE
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a(4) = 1568397607 = 199a(3) + a(2) = 199*7881196+ 39603=((199+sqrt(39605))/2)^4 + ( (199-sqrt(39605))/2)^4 =1568397606.9999999993624065 + 0.0000000006375934=1568397607.
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CROSSREFS
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Cf. A000032.
Adjacent sequences: A089769 A089770 A089771 this_sequence A089773 A089774 A089775
Sequence in context: A123100 A033147 A124339 this_sequence A110899 A012600 A092700
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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), Jan 09 2004
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