Sums of squares of Tetranacci numbers: A generating function approach
Helmut Prodinger, Sarah J. Selkirk
TL;DR
This paper derives explicit formulas for sums of Tetranacci numbers using generating functions, and provides a Binet-type formula for generalized Fibonacci numbers through factorization of their generating functions.
Contribution
It introduces a generating function approach to sum Tetranacci numbers and derives a Binet-type formula for generalized Fibonacci numbers, expanding analytical tools for these sequences.
Findings
Explicit sum formulas for Tetranacci numbers
Binet-type formula for generalized Fibonacci numbers
Use of generating functions and Hadamard product
Abstract
It is demonstrated how an explicit expression of the (partial) sum of Tetranacci numbers can be found and proved using generating functions and the Hadamard product. We also provide a Binet-type formula for generalized Fibonacci numbers, by explicitly factoring the denominator of their generating functions.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Theories and Applications · Advanced Mathematical Identities