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Search: id:A086927
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| A086927 |
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a(n) = 10a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 10. |
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+0
3
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| 2, 10, 102, 1030, 10402, 105050, 1060902, 10714070, 108201602, 1092730090, 11035502502, 111447755110, 1125513053602, 11366578291130, 114791295964902, 1159279537940150, 11707586675366402
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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 (5+sqrt(26)) =10.099019... a(0)/a(1)=2/10; a(1)/a(2)=10/102; a(2)/a(3)=102/1030; a(3)/a(4)=1030/10402; ... etc. Lim a(n)/a(n+1) as n approaches infinity = 0.099019... = 1/(5+sqrt(26)) = (sqrt(26)-5).
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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) = (5+sqrt(26))^n + (5-sqrt(26))^n.
G.f.: (2-10x)/(1-10x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 20 2008]
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EXAMPLE
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a(4) = 10402 = 10a(3) + a(2) = 10*1030 + 102 = (5+sqrt(26))^4 + (5-sqrt(26))^4 =
10401.999903 + 0.000097 = 10402
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CROSSREFS
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Cf. A036336.
Sequence in context: A074109 A036336 A070842 this_sequence A135058 A154256 A005799
Adjacent sequences: A086924 A086925 A086926 this_sequence A086928 A086929 A086930
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KEYWORD
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easy,nonn,more
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AUTHOR
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Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Sep 21 2003
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