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Search: id:A087800
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| A087800 |
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a(n) =12a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 12, a(n) = (6+sqrt(35))^n + (6-sqrt(35))^n. |
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+0
2
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| 2, 12, 142, 1692, 20162, 240252, 2862862, 34114092, 406506242, 4843960812, 57721023502, 687808321212, 8195978831042, 97663937651292, 1163771272984462, 13867591338162252, 165247324784962562, 1969100306081388492
(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 (6+sqrt(35)) = 11.9160797... a(0)/a(1)=2/12; a(1)/a(2)=12/142; a(2)/a(3)=142/1692; a(3)/a(4)=1692/20162; ... etc. Lim a(n)/a(n+1) as n approaches infinity = 0.0839202... = 1/(6+sqrt(35)) = (6-sqrt(35)).
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
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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G.f.: (2-12x)/(1-12x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 17 2008]
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EXAMPLE
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a(4) = 20162 = 12a(3) - a(2) = 12*1692 - 142 =(6+sqrt(35))^4 + (6-sqrt(35))^4 =
20161.9999504 + 0.00004959 = 20162.
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MATHEMATICA
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a[0] = 2; a[1] = 12; a[n_] := 12a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 17}] (from Robert G. Wilson v Jan 30 2004)
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PROGRAM
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sage: [lucas_number2(n, 12, 1) for n in xrange(1, 20)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008
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CROSSREFS
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Cf. A009747, A086928, A001927.
Equals 2*A023038(n).
Sequence in context: A119819 A093543 A091144 this_sequence A009747 A067601 A052740
Adjacent sequences: A087797 A087798 A087799 this_sequence A087801 A087802 A087803
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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 11 2003
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