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A090300
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a(n) = 14a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 14.
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0
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2, 14, 198, 2786, 39202, 551614, 7761798, 109216786, 1536796802, 21624372014, 304278004998, 4281516441986, 60245508192802, 847718631141214, 11928306344169798, 167844007449518386, 2361744410637427202
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(n+1)/a(n) converges to (7+sqrt(50)) = 14.071067811... Lim a(n)/a(n+1) as n approaches infinity = 0.071067811... = 1/(7+sqrt(50)) = (sqrt(50)-7). Lim a(n+1)/a(n) as n approaches infinity = 14.071067811... = (7+sqrt(50)) = 1/(sqrt(50)-7).
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LINKS
| Tanya Khovanova, Recursive Sequences
Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)
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FORMULA
| a(n) =14a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 14. a(n) = (7+sqrt(50))^n + (7-sqrt(50))^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.: (2-14*x)/(1-14*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 02 2008]
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EXAMPLE
| a(4) = 39202 = 14a(3) + a(2) = 14*2786+ 198 = (7+sqrt(50))^4 + (7-sqrt(50))^4 =39201.999974491 + 0.000025508 = 39202.
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CROSSREFS
| Cf. A050012.
Sequence in context: A132611 A156327 A047796 * A102224 A123543 A054652
Adjacent sequences: A090297 A090298 A090299 * A090301 A090302 A090303
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KEYWORD
| easy,nonn
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AUTHOR
| Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 25 2004
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EXTENSIONS
| More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 14 2004
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