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Search: id:A090308
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| A090308 |
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a(n) = 19a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 19. |
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+0
1
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| 2, 19, 363, 6916, 131767, 2510489, 47831058, 911300591, 17362542287, 330799604044, 6302555019123, 120079344967381, 2287810109399362, 43588471423555259, 830468767156949283, 15822495047405591636
(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 (19+sqrt(365))/2 = 19.052486... Lim a(n)/a(n+1) as n approaches infinity = 0.052486... = 2/(19+sqrt(365)) = (sqrt(365)-19)/2. Lim a(n+1)/a(n) as n approaches infinity = 19.052486... = (19+sqrt(365))/2 = 2/(sqrt(365)-19).
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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) =19a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 19. a(n) = ((19+sqrt(365))/2)^n + ((19-sqrt(365))/2)^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.: (2-19x)/(1-19x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 02 2008]
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EXAMPLE
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a(4) = 131767 = 19a(3) + a(2) = 19*6916+ 363=((19+sqrt(365))/2)^4 + ((19-sqrt(365))/2)^4 = 131766.9999924108 + 0.0000075891 = 131767.
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CROSSREFS
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Cf. A049270.
Sequence in context: A119773 A137647 A078369 this_sequence A110818 A155927 A120420
Adjacent sequences: A090305 A090306 A090307 this_sequence A090309 A090310 A090311
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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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