论文标题
总结一个普遍的佩尔数字
Summing a family of generalized Pell numbers
论文作者
论文摘要
Bród\ cite {dorota}最近引入和研究了一个新的广义佩尔数字。这些数字作为斐波那契数，是一个双层公式。使用此情况，可以明确地概括一般的Pell数字的任意权力的部分总和。为此，作为第一步，电源$ p_n^l $表示为$ p_ {mn} $的线性组合。 然后，使用生成功能可以管理此类表达式的求和。由于新家庭包含一个参数$ r = 2^r $，因此相关的操作非常涉及，计算机代数产生了巨大的表达式，有时并不容易处理。
A new family of generalized Pell numbers was recently introduced and studied by Bród \cite{Dorota}. These number possess, as Fibonacci numbers, a Binet formula. Using this, partial sums of arbitrary powers of generalized Pell numbers can be summed explicitly. For this, as a first step, a power $P_n^l$ is expressed as a linear combination of $P_{mn}$. The summation of such expressions is then manageable using generating functions. Since the new family contains a parameter $R=2^r$, the relevant manipulations are quite involved, and computer algebra produced huge expressions that where not trivial to handle at times.
