Algebra Representation Of Special Sequences And Application In Magic Square Construction

The research enthusiasm of special sequences is keeping on for a long time.Although there have been a lot of Fibonacci Sequences research findings,special sequences types are different.Therefore,there are many things worth exploring.The special matrix,magic square,is rich,rigorous,and characteristic.There are rich achievements at present,however,this mysterious infinite square needs to continue to explore because of too many issues.When some special subsequences combine with magic square,there are some new findings.The algebraic representation of four kinds of special sequences is given by the analogy of Fibonacci Sequences,Then a new methods of magic square matrix construction is discovered;Finally,the linear retention of magic square matrix is studied.This paper is mainly done from the following three aspects.First,the research status and related research achievements of the three aspects of the special sequences,the magic square construction and the retention have been introduced.As a result,the significance and necessity of this research are found.Second,studies on algebraic representation of four special sequences.At first,the new definitions of four special sequences are given.Then the general representation,matrix representation and determinant representation of general formula are discovered.Finally,the matrix expression of the recursive relation is obtained.Third,the definition and characters of magic square are given.And then a new method of magic square matrix construction is discovered,namely,matrices construction method and functions construction method.Finally,the magic square matrix is constructed with limited subsequences of special sequences,and the linear retention of magic square matrix is studied.