OFFSET
0,3
COMMENTS
Binet form: with a = 4/(1 + sqrt(3)); b = 4/(1 - sqrt(3)); we have a(n)=(a^n - b^n)/(a - b).
Alternative expressions for the roots are -2 +- 2*sqrt(3).
Limiting ratio a(n+1)/a(n) is:-5.464101615137755== -2-2*sqrt(3).
LINKS
Nathaniel Johnston, Table of n, a(n) for n = 0..500
FORMULA
a(0)=0, a(1)=1, a(n) = -4a(n-1) + 8a(n-2).
a(0)=0, a(n) = (-2)^(n-1)*A002605(n).
MATHEMATICA
a = 4/(1 + Sqrt[3]); b = 4/(1 - Sqrt[3]);
f[n_] = (a^n - b^n)/(a - b);
Table[FullSimplify[f[n]], {n, 0, 30}]
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Roger L. Bagula, Nov 28 2010
EXTENSIONS
Correction of the Mathematica code and better name by Joerg Arndt.
Formulae and edited by Ralf Stephan, Nov 27 2010
STATUS
approved