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 A086927 a(n) = 10*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 10. 5
 2, 10, 102, 1030, 10402, 105050, 1060902, 10714070, 108201602, 1092730090, 11035502502, 111447755110, 1125513053602, 11366578291130, 114791295964902, 1159279537940150, 11707586675366402, 118235146291604170 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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). REFERENCES 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 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (10,1). FORMULA a(n) = (5+sqrt(26))^n + (5-sqrt(26))^n. G.f.: (2-10*x)/(1-10*x-x^2). - Philippe Deléham, Nov 20 2008 EXAMPLE a(4) = 10402 = 10*a(3) + a(2) = 10*1030 + 102 = (5+sqrt(26))^4 + (5-sqrt(26))^4 =  10401.999903 + 0.000097 = 10402. MATHEMATICA RecurrenceTable[{a[0] == 2, a[1] == 10, a[n] == 10 a[n-1] + a[n-2]}, a, {n, 30}] (* Vincenzo Librandi, Sep 19 2016 *) PROG (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 CROSSREFS Cf. A036336. Sequence in context: A291101 A036336 A070842 * A135058 A154256 A304319 Adjacent sequences:  A086924 A086925 A086926 * A086928 A086929 A086930 KEYWORD nonn,easy AUTHOR Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Sep 21 2003 EXTENSIONS More terms from Jon E. Schoenfield, May 15 2010 STATUS approved

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Last modified December 10 12:33 EST 2018. Contains 318047 sequences. (Running on oeis4.)