Smarandache-Pascal派生逆序列的几个恒等式

Some identities on the Smarandache-Pascal inverse derived sequence

引入了Smarandache-Pascal派生逆序列的定义,并利用初等及组合方法讨论了Smarandache-Pascal派生逆序列的性质,得到几个有趣的恒等式,从而证明了如果任何基序列{Tn}是一个二阶线性递推序列,那么它所产生的Smarandache-Pascal派生逆序列{bn}也是一个二阶线性递推数列,且当基数列{Tdn+1}是一个二阶线性递推数列{Tn}的子列时,则它的派生逆序列{bn}的线性表示式更为简洁.

Smarandache-Pascal inverse-derived sequence is introduced, the properties of the Smarandache-Pascal inverse-derived sequence are studied, some interesting identities are obtained by using the elementary and combinational method, and it is proved that if the base sequence { Tn } is a second-order linear recurrence sequence, then its Smarandache-Pascal inverse-derived subsequence is a second-order linear recurrence sequence. Moreover,if the base sequence { Tdn＋t } is a subset of the second-order linear recurrence sequence { Tn }, then its Smarandache-Pascal inverse-derived sequence {bn } has a simple linear recurrence expression.