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Search: id:A090301
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| A090301 |
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a(n) = 15a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 15. |
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+0
1
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| 2, 15, 227, 3420, 51527, 776325, 11696402, 176222355, 2655031727, 40001698260, 602680505627, 9080209282665, 136805819745602, 2061167505466695, 31054318401746027, 467875943531657100, 7049193471376602527
(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 (15+sqrt(229))/2 = 15.066372... Lim a(n)/a(n+1) as n approaches infinity = 0.066372... = 2/(15+sqrt(229)) = (sqrt(229)-15)/2. Lim a(n+1)/a(n) as n approaches infinity = 15.066372... = (15+sqrt(229))/2 = 2/(sqrt(229)-15).
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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) =15a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 15. a(n) = ((15+sqrt(229))/2)^n + ((15-sqrt(229))/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) = 51527 = 15a(3) + a(2) = 15*3420+ 227=((15+sqrt(229))/2)^4 + ((15-sqrt(229))/2)^4 = 51526.9999805 + 0.0000194 =51527
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CROSSREFS
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Cf. A058087, A071416.
Sequence in context: A140054 A099085 A078365 this_sequence A097628 A102555 A076111
Adjacent sequences: A090298 A090299 A090300 this_sequence A090302 A090303 A090304
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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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