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A086927
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a(n) = 10*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 10.
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17
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2, 10, 102, 1030, 10402, 105050, 1060902, 10714070, 108201602, 1092730090, 11035502502, 111447755110, 1125513053602, 11366578291130, 114791295964902, 1159279537940150, 11707586675366402, 118235146291604170
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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 (5+sqrt(26)) = 10.099019...
Lim a(n)/a(n+1) as n approaches infinity = 0.099019... = 1/(5+sqrt(26)) = (sqrt(26)-5).
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REFERENCES
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Stefano Arnone, C Falcolini, F Moauro, M Siccardi, On Numbers in Different Bases: Symmetries and a Conjecture, Experimental Mathematics, Vol 26 2016, pp 197-209; http://dx.doi.org/10.1080/10586458.2016.1149125
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LINKS
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FORMULA
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a(n) = (5+sqrt(26))^n + (5-sqrt(26))^n.
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EXAMPLE
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a(4) = 10402 = 10*a(3) + a(2) = 10*1030 + 102 = (5+sqrt(26))^4 + (5-sqrt(26))^4 = 10401.999903 + 0.000097 = 10402.
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MATHEMATICA
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RecurrenceTable[{a[0] == 2, a[1] == 10, a[n] == 10 a[n-1] + a[n-2]}, a, {n, 30}] (* Vincenzo Librandi, Sep 19 2016 *)
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PROG
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(Magma) I:=[2, 10]; [n le 2 select I[n] else 10*Self(n-1)+Self(n-2): n in [1..30]]; // Vincenzo Librandi, Sep 19 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Sep 21 2003
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EXTENSIONS
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STATUS
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approved
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