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A065705
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Lucas numbers L(10*n).
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2
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2, 123, 15127, 1860498, 228826127, 28143753123, 3461452808002, 425730551631123, 52361396397820127, 6440026026380244498, 792070839848372253127, 97418273275323406890123, 11981655542024930675232002, 1473646213395791149646646123, 181246502592140286475862241127
(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 (123+sqrt(15125))/2 = 122.9918693812... a(0)/a(1)=2/123; a(1)/a(2)=123/15127; a(2)/a(3)= 15127/1860498; a(3)/a(4)= 1860498/228826127; ... etc. Lim a(n)/a(n+1) as n approaches infinity = 0.00813061875578... = 2/(123+sqrt(15125)) = (123-sqrt(15125))/2.
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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) = 123*a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 123.
a(n) = ((123+sqrt(15125))/2)^n + ((123-sqrt(15125))/2)^n.
a(n))^2 = a(2*n) + 2.
G.f.: (2-123*x)/(1-123*x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]
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EXAMPLE
| a(4) = 228826127 = 123*a(3) - a(2) = 123*1860498 - 15127=((123+sqrt(15125))/2)^4 + ( (123-sqrt(15125))/2)^4 =228826126.99999999562986 + 0.00000000437013 = 228826127.
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PROG
| (MAGMA) [ Lucas(10*n) : n in [0..90]]; // Vincenzo Librandi, Apr 14 2011
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CROSSREFS
| Cf. A000032.
a(n) = A000032(10n).
Sequence in context: A056638 A024244 A088055 * A012870 A183720 A042921
Adjacent sequences: A065702 A065703 A065704 * A065706 A065707 A065708
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KEYWORD
| easy,nonn
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AUTHOR
| Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Oct 25 2003
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EXTENSIONS
| More terms from Vincenzo Librandi, Apr 14 2011
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