| Summary: | 碩士 === 淡江大學 === 數學學系碩士在職專班 === 106 === For solving n-th recurrence relations ,many researches use formal power series or characteristic polynomial. In this research,we use matrix methods with characteristic polynomial to discuss different properties in recurrence relations.This topic discuss Perrin sequence at first. Next,we define a new sequence “Q_n sequence”,and try to find the relation between “Perrin sequence” and “ Q_n sequence”.Finally, we extend “Perrin sequence” and “ Q_n sequence” the 3-th recurrence relations to the n-th recurrence relations,and we named them as “n-step Perrin sequence” and “n-step Q_n sequence,{T_n} ”.
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