OFFSET
0,1
COMMENTS
a(n+1)/a(n) converges to (7+sqrt(50)) = 14.071067811...
Lim_{n->infinity} a(n)/a(n+1) = 0.071067811... = 1/(7+sqrt(50)) = sqrt(50) - 7.
Lim_{n->infinity} a(n+1)/a(n) = 14.071067811... = (7+sqrt(50)) = 1/(sqrt(50) - 7).
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..870
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (14, 1).
FORMULA
a(n) = 14*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 14.
a(n) = (7+sqrt(50))^n + (7-sqrt(50))^n.
(a(n))^2 = a(2n)-2 if n = 1, 3, 5, ...; (a(n))^2 = a(2n)+2 if n = 2, 4, 6, ....
G.f.: (2-14*x)/(1-14*x-x^2). - Philippe Deléham, Nov 02 2008
EXAMPLE
a(4) = 39202 = 14*a(3) + a(2) = 14*2786 + 198 = (7+sqrt(50))^4 + (7-sqrt(50))^4 = 39201.999974491 + 0.000025508 = 39202.
MATHEMATICA
LinearRecurrence[{14, 1}, {2, 14}, 20] (* Harvey P. Dale, Jul 12 2020 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 25 2004
EXTENSIONS
More terms from Ray Chandler, Feb 14 2004
STATUS
approved