OFFSET
0,3
COMMENTS
a(n)/a(n-1) -> (1 + sqrt(5))/2 = golden ratio (A001622), so that a( ) has the growth rate of the Fibonacci numbers (A000045).
Therefore the terms are all >= 0. - Georg Fischer, Feb 19 2019
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (1, 3, -2, -2)
FORMULA
a(n) = a(n-1) + 3*a(n-2) - 2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = 0, a(2) = 2, a(3) = 1. [Corrected by Colin Barker, Dec 15 2017]
G.f.: -(((-2 + x) x^2)/((-1 + x + x^2) (-1 + 2 x^2))).
From Colin Barker, Dec 15 2017: (Start)
a(n) = -2^((n-3)/2+3/2) + ((1-sqrt(5))/2)^(n+1) + (2/(1+sqrt(5)))^(-n-1) for n even.
a(n) = -3*2^((n-3)/2+1) + ((1-sqrt(5))/2)^(n+1) + (2/(1+sqrt(5)))^(-n-1) for n odd.
(End)
MATHEMATICA
LinearRecurrence[{1, 3, -2, -2}, {0, 0, 2, 1}, 100]
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Clark Kimberling, Dec 01 2017
STATUS
approved