OFFSET
1,2
COMMENTS
De Moivres formula : a(n)=(r^n-s^n)/(r-s), for r>s gives sequences with integers if r and s are conjugates. With r=2+sqrt(17) and s=2-sqrt(17), a(n+1)/a(n) converges to 2+sqrt(17).
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4,13).
FORMULA
a(n) = ((2+sqrt(17))^n-(2-sqrt(17))^n)/(2*sqrt(17)).
G.f.: x/(1-4*x-13*x^2). - Bruno Berselli, Nov 15 2011
EXAMPLE
a(3) = 4*4+13*1 = 29.
MATHEMATICA
LinearRecurrence[{4, 13}, {1, 4}, 50]
PROG
(Haskell)
a200069 n = a200069_list !! (n-1)
a200069_list = 1 : 4 : zipWith (+)
(map (* 4) $ tail a200069_list) (map (* 13) a200069_list)
-- Reinhard Zumkeller, Nov 15 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Sture Sjöstedt, Nov 13 2011
EXTENSIONS
More terms from Bruno Berselli, Nov 15 2011
STATUS
approved