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A090247
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a(n) = 26a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 26.
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0
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2, 26, 674, 17498, 454274, 11793626, 306180002, 7948886426, 206364867074, 5357537657498, 139089614227874, 3610972432267226, 93746193624720002, 2433790061810452826, 63184795413447053474, 1640370890687812937498
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OFFSET
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0,1
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COMMENTS
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a(n+1)/a(n) converges to (13+sqrt(168)) =25.9614813... Lim a(n)/a(n+1) as n approaches infinity = 0.0385186... = 1/(13+sqrt(168)) = (13-sqrt(168)). Lim a(n+1)/a(n) as n approaches infinity = 25.9614813... = (13+sqrt(168)) = 1/(13-sqrt(168)). Lim a(n)/a(n+1) = 26 - Lim a(n+1)/a(n).
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LINKS
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Table of n, a(n) for n=0..15.
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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a(n) =26a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 26. a(n) = (13+sqrt(168))^n + (13-sqrt(168))^n. (a(n))^2 =a(2n)+2.
G.f.: (2-26x)/(1-26x+x^2). [From Philippe DELEHAM, Nov 02 2008]
G.f.: (2-26*x)/(1-26*x+x^2). [From Philippe DELEHAM, Nov 02 2008]
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EXAMPLE
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a(4) = 454274 = 26a(3) - a(2) = 26*17498 - 674 =(13+sqrt(168))^4 + (13-sqrt(168))^4 =454273.9999977986 + 0.0000022013 =454274.
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MATHEMATICA
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a[0] = 2; a[1] = 26; a[n_] := 26a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 15}] (from Robert G. Wilson v Jan 30 2004)
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PROG
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sage: [lucas_number2(n, 26, 1) for n in xrange(0, 16)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 27 2008
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CROSSREFS
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Cf. A032000, A019586.
Sequence in context: A137100 A216254 A177316 * A206601 A156211 A156212
Adjacent sequences: A090244 A090245 A090246 * A090248 A090249 A090250
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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 24 2004
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EXTENSIONS
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More terms from Robert G. Wilson v, Jan 30 2004
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STATUS
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approved
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