一类广义Tribonacci数列的性质与应用

Property and Application of One Class of GeneralizedTribonacci Sequence

摘要: 在Tribonacci数列的基础上推广得到一类更广泛的数列——广义Tribonacci数列。分别利用组合数学和矩阵论中的方法与技巧对该数列进行了分析研究，求得了广义Tribonacci数列通项的多种表示形式。并利用其定义推导得到广义Tribonacci数列的性质定理。同时应用广义Tribonacci数列的通项公式和性质定理解决了实际问题。进一步揭示了广义Tribonacci数列与实际生活中的现象是紧密联系的。

Abstract: This paper obtains a more extensive sequence based on the Tribonacci sequence —— the generalized Tribonacci sequence. Using the combinatorics and matrix methods and techniques, a variety of repre-sentations of the general term formula of the generalized Tribonacci sequence are obtained, Properties and theorems of the generalized Tribonacci sequence are acquired in according to its definition. The application of Tribonacci sequence is also involved. Has further promulgated in the generalized Tribonacci sequence and the practical life phenomenon is the close relation.