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Search: id:A090305
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| A090305 |
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a(n) = 16a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 16. |
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+0
1
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| 2, 16, 258, 4144, 66562, 1069136, 17172738, 275832944, 4430499842, 71163830416, 1143051786498, 18359992414384, 294902930416642, 4736806879080656, 76083812995707138, 1222077814810394864, 19629328849962024962
(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 (8+sqrt(65)) = 16.0622577... Lim a(n)/a(n+1) as n approaches infinity = 0.0622577... = 1/(8+sqrt(65)) = (sqrt(65)-8). Lim a(n+1)/a(n) as n approaches infinity = 16.0622577... = (8+sqrt(65)) = 1/(sqrt(65)-8).
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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) =16a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 16. a(n) = (8+sqrt(65))^n + (8-sqrt(65))^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.: (2-16x)/(1-16x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 02 2008]
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EXAMPLE
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a(4) = 66562 = 16a(3) + a(2) = 16*4144+ 258 = (8+sqrt(65))^4 + (8-sqrt(65))^4 =66561.99998497 + 0.00001502 = 66562.
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CROSSREFS
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Cf. A002070, A015910.
Sequence in context: A108242 A140307 A114039 this_sequence A050974 A012188 A009764
Adjacent sequences: A090302 A090303 A090304 this_sequence A090306 A090307 A090308
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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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