一类广义Fibonacci数列的通项及其求和

General Term and sum of a kind of Generalized Fibonacci Sequence

研究如下广义Fibonacci数列{F(n)}:F(n)=k F(n-1)+m F(n-2),F(0)=a,F(1)=b,利用矩阵的特征值和特征向量得到其通项表达式,并讨论当m=2k^2时该数列的通项、偶数项、奇数项和交错项的和.

In this paper, we investigated the following generalized Fibonaeci sequence {F（n）}：F（n）=k F（n-1）＋m F（n-2）,F（0）=a,F（1）=b,Using the eigenvalue and eigenvector of matrix, we obtained its general term. When m = 2k^2, we discussed the sums of its general terms, even terms, odd terms and alternating terms.