Generalized Factoriangular Numbers And Factoriangular Triangles
Volume 1 - Issue 5, November 2017 Edition
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Author(s)
Romer C. Castillo
Keywords
factoriangular number, factoriangular triangle, generalized factoriangular number, integer sequence, recreational mathematics
Abstract
A factoriangular number is defined as the sum of corresponding factorial and triangular number. This paper aims to generalize this number as sum of any factorial and any triangular number and explore such generalization. This study is a basic research in number theory that uses mathematical exposition and exploration. The generalized factoriangular number is of the form , where is the factorial of a natural number and is the triangular number. When , the sum is an ordinary factoriangular number. A consequence of the generalization is the creation of interesting Pascal-like triangles that are hereby called factoriangular triangles and formation of their corresponding integer sequences. Generalized factoriangular numbers and factoriangular triangles can be utilized as recreational mathematics for students. Further generalizations of factoriangular number and expositions on factoriangular triangles can be done next.
References
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