OFFSET
0,1
COMMENTS
Lim_{n->infinity} a(n)/a(n-1) = 2.
LINKS
Index entries for linear recurrences with constant coefficients, signature (3, -1, -2).
FORMULA
G.f.: (3 - 6*x + 2*x^2) / (1 - 3*x + x^2 + 2*x^3)
a(n) = p^n + q^n + r^n, where p = (1+sqrt(5))/2, q = (1-sqrt(5))/2, and r = 2*p^n + q^n = L(n) = A000032(n), so a(n) = L(n) + 2^n
a(0)=3, a(1)=3, a(2)=7 and a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) for n >= 3.
EXAMPLE
a(6) = 82 = L(6) + 2^6 = 18 + 64.
a(7) = 157 = 3*82 - 43 - 2*23 = 246 - 43 - 46.
PROG
(Magma) [2^n+Lucas(n): n in [0..50]]; // Vincenzo Librandi, Apr 14 2011
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Miklos Kristof, Nov 25 2003
STATUS
approved