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A090316
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a(n) = 24a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 24.
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2, 24, 578, 13896, 334082, 8031864, 193098818, 4642403496, 111610782722, 2683301188824, 64510839314498, 1550943444736776, 37287153512997122, 896442627756667704, 21551910219673022018, 518142287899909196136
(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 (12+sqrt(145)) = 24.0415945... Lim a(n)/a(n+1) as n approaches infinity = 0.0415945... = 1/(12+sqrt(145)) = (sqrt(145)-12). Lim a(n+1)/a(n) as n approaches infinity = 24.0415945... = (12+sqrt(145)) = 1/(sqrt(145)-12).
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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) =24a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 24. a(n) = (12+sqrt(145))^n + (12-sqrt(145))^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.: (2-24x)/(1-24x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 02 2008]
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EXAMPLE
| a(4) =334082 = 24a(3) + a(2) = 24*13896+ 578 = (12+sqrt(145))^4 + (12-sqrt(145))^4 = 334081.99999700672 + 0.00000299327 = 334082.
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CROSSREFS
| Cf. A058168, A056949.
Sequence in context: A170904 A090732 A014298 * A128578 A186632 A089835
Adjacent sequences: A090313 A090314 A090315 * A090317 A090318 A090319
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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
Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006
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