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Search: id:A090313
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| A090313 |
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a(n) = 22a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 22. |
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+0
1
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| 2, 22, 486, 10714, 236194, 5206982, 114789798, 2530582538, 55787605634, 1229857906486, 27112661548326, 597708411969658, 13176697724880802, 290485058359347302, 6403847981630521446, 141175140654230819114
(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 (11+sqrt(122)) = 22.045361... Lim a(n)/a(n+1) as n approaches infinity = 0.045361... = 1/(11+sqrt(122)) = (sqrt(122)-11). Lim a(n+1)/a(n) as n approaches infinity = 22.045361... = (11+sqrt(122)) = 1/(sqrt(122)-11).
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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) =22a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 22. a(n) = (11+sqrt(122))^n + (11-sqrt(122))^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.: (2-22x)/(1-22x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 02 2008]
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EXAMPLE
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a(4) =236194 = 22a(3) + a(2) = 22*10714+ 486 = (11+sqrt(122))^4 + (11-sqrt(122))^4 = 236193.999995766 + 0.000004233 = 236194.
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CROSSREFS
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Cf. A079219.
Sequence in context: A084949 A137076 A090730 this_sequence A110129 A120419 A132568
Adjacent sequences: A090310 A090311 A090312 this_sequence A090314 A090315 A090316
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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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