Let s_{k} denote the sum of the k th powers of the roots of the polynomial x^{3}-5 x^{2}+8 x-13. In particular, s_{0}=3, s_{1}=5, and s_{2}=9. Let a, b, and c be real numbers such that s_{k+1}= a s_{k}+b s_{k-1}+c s_{k-2} for k=2,3, \ldots What is a+b+c ?
Answer Choices
A. -6
B. 0
C. 6
D. 10
E. 26