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
a(n) = 2*A088320(n). - R. J. Mathar, Feb 06 2020
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
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