A086927 a(n) = 10*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 10.

2, 10, 102, 1030, 10402, 105050, 1060902, 10714070, 108201602, 1092730090, 11035502502, 111447755110, 1125513053602, 11366578291130, 114791295964902, 1159279537940150, 11707586675366402, 118235146291604170

Offset: 0

Author

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Sep 21 2003

Keywords

• nonn
• easy

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).

Examples

			a(4) = 10402 = 10*a(3) + a(2) = 10*1030 + 102 = (5+sqrt(26))^4 + (5-sqrt(26))^4 =  10401.999903 + 0.000097 = 10402.
		

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 recurrences a(n) = k*a(n - 1) +/- a(n - 2)
• Index entries for linear recurrences with constant coefficients, signature (10,1).

Crossrefs

Cf. A036336.

Programs

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

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 *)

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

Extensions

More terms from Jon E. Schoenfield, May 15 2010