OFFSET
0,3
COMMENTS
Jacobsthal-Lucas numbers less 1.
For n >= 1, a(n) is also the number of periodic points of period n of the Period Doubling and the Thue-Morse Chain. [Natascha Neumaerker (naneumae(AT)math.uni-bielefeld.de), Apr 06 2009]
LINKS
FORMULA
G.f.: (1-2x+3x^2)/((1-x)(1-x-2x^2)) = (1-2x+3x^2)/((1-x^2)(1-2x)).
a(n) = A014551(n)-1.
zeta(z) = (1-z)/((1+z)(1-2z)). [Natascha Neumaerker (naneumae(AT)math.uni-bielefeld.de), Apr 06 2009]
a(n) = 2*a(n-1)+a(n-2)-2*a(n-3). - Wesley Ivan Hurt, Jun 09 2023
MATHEMATICA
LinearRecurrence[{2, 1, -2}, {1, 0, 4}, 40] (* Harvey P. Dale, Nov 07 2017 *)
PROG
(PARI) a(n)=2^n+(-1)^n-1 \\ Charles R Greathouse IV, May 09 2016
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 15 2004
STATUS
approved