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Search: id:A090309
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| A090309 |
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a(n) = 20a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 20. |
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2
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| 2, 20, 402, 8060, 161602, 3240100, 64963602, 1302512140, 26115206402, 523606640180, 10498248010002, 210488566840220, 4220269584814402, 84615880263128260, 1696537874847379602, 34015373377210720300
(list; graph; listen)
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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 (10+sqrt(101)) = 20.0498756... Lim a(n)/a(n+1) as n approaches infinity = 0.0498756... = 1/(10+sqrt(101)) = (sqrt(101)-10). Lim a(n+1)/a(n) as n approaches infinity = 20.0498756... = (10+sqrt(101)) = 1/(sqrt(101)-10).
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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) =20a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 20. a(n) = (10+sqrt(101))^n + (10-sqrt(101))^n. (a(n))^2 =a(2n)-2 if n=1, 3, 5..., (a(n))^2 =a(2n)+2 if n=2, 4, 6....
G.f.: (2-20*x)/(1-20*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 02 2008]
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EXAMPLE
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a(4) =161602 = 20a(3) + a(2) = 20*8060+ 402 = (10+sqrt(101))^4 + (10-sqrt(101))^4 =161601.999993811 + 0.000006188 = 161602.
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CROSSREFS
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Cf. A002116.
Sequence in context: A009236 A078698 A090728 this_sequence A002116 A058346 A165554
Adjacent sequences: A090306 A090307 A090308 this_sequence A090310 A090311 A090312
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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 25 2004
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EXTENSIONS
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More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 14 2004
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