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Search: id:A087215
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| A087215 |
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Lucas(6n): a(n) = 18a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 18. |
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2
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| 2, 18, 322, 5778, 103682, 1860498, 33385282, 599074578, 10749957122, 192900153618, 3461452808002, 62113250390418, 1114577054219522, 20000273725560978, 358890350005878082, 6440026026380244498
(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 (9+sqrt(80)) = 17.9442719... a(0)/a(1)=2/18; a(1)/a(2)=18/322; a(2)/a(3)=322/5778; a(3)/a(4)=5778/103682; ... etc. Lim a(n)/a(n+1) as n approaches infinity = 0.05572809000084... = 1/(9+sqrt(80)) = (9-sqrt(80)).
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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) =18a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 18, a(n) = (9+sqrt(80))^n + (9-sqrt(80))^n.
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EXAMPLE
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a(4) = 103682 = 18a(3) - a(2) = 18*5778 - 322 =(9+sqrt(80))^4 + (9-sqrt(80))^4 =
103681.99999035512 + 0.00000964487 = 103682.
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MATHEMATICA
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a[0] = 2; a[1] = 18; a[n_] := 18a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 15}] (from Robert G. Wilson v Jan 30 2004)
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CROSSREFS
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Cf. A000032, A074919.
a(n) = A000032(6n) = Lucas numbers L(6n).
Adjacent sequences: A087212 A087213 A087214 this_sequence A087216 A087217 A087218
Sequence in context: A123385 A121564 A092563 this_sequence A090307 A123311 A132911
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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), Oct 19 2003
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