关于“3-1”数列的几个性质

Some Properties of '3-1' Sequence

研究了Lucian Tutescu提出的50多个数论问题中的第四个问题‘3-1’数列的性质,运用初等数论和组合数学的方法,得出了‘3-1’数列的一般项公式、生成函数、前n项部分和公式以及递归公式,结果表明在数论中,许多特殊数列都有其规律性,并可以用同样的方法加以研究..

The properties of sequence '3-1',the fourth of 50 plus problems raised by Lucian Tutscu,a great Romanian expert of number theory at Fratii Buzesti University,were studied.With the application of primary number theory and methods in combinatorics,formula of the general term of sequence '3-1' were obtained,together with its generative function,formula for the partial sum of its beginning nth-terms,and its recursive formula.The result shows that there are rules for many special sequences,which can be studied with the same methods.