OFFSET
0,1
COMMENTS
a(n+1)/a(n) converges to (29+sqrt(845))/2 = 29.0344418537...
a(0)/a(1) = 2/29, a(1)/a(2) = 29/843, a(2)/a(3) = 843/24476, a(3)/a(4) = 24476/710647, etc.
Lim_{n->infinity} a(n)/a(n+1) = 0.0344418537... = 2/(29+sqrt(845)) = (sqrt(845)-29)/2.
LINKS
FORMULA
a(n) = 29*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 29.
a(n) = ((29 + sqrt(845))/2)^n + ((29 - sqrt(845))/2)^n.
a(n)^2 = a(2n) - 2 for n = 1, 3, 5, ...;
a(n)^2 = a(2n) + 2 for n = 2, 4, 6, ....
G.f.: (2-29*x)/(1-29*x-x^2). - Philippe Deléham, Nov 02 2008
EXAMPLE
a(4) = 710647 = 29*a(3) + a(2) = 29*24476 + 843 = ((29+sqrt(845))/2)^4 + ((29-sqrt(845))/2)^4 = 710646.9999985928... + 0.0000014071... = 710647.
MATHEMATICA
LucasL[7Range[0, 20]] (* or *) LinearRecurrence[{29, 1}, {2, 29}, 20] (* Harvey P. Dale, Nov 22 2011 *)
PROG
(Magma) [ Lucas(7*n) : n in [0..100]]; // Vincenzo Librandi, Apr 14 2011
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Oct 19 2003
EXTENSIONS
More terms from Ray Chandler, Feb 14 2004
More terms from Vincenzo Librandi, Apr 14 2011
STATUS
approved