IDEAS home Printed from https://ideas.repec.org/a/ajp/edwast/v9y2025i3p891-904id5378.html
   My bibliography  Save this article

Mathematical explorations on the sequence of factoriangular numbers: Extending the results on generalizations

Author

Listed:
  • Romer C. Castillo

Abstract

A factoriangular number is formed by adding a factorial and a triangular number. If corresponding factorials and triangular numbers are added, the results are n-factoriangular numbers. Other factoriangular numbers are called (n,k)-factoriangular numbers, n(m)-factoriangular numbers, (n(m),k(m))-factoriangular numbers, and (n(a),k(b))-factoriangular numbers. The main objective of this study is to explore the sequence of (n(m),k(m))-factoriangular numbers and the sequence of (n(a),k(b))-factoriangular numbers as generalizations of the sequence of n-factoriangular numbers. This research is a discipline-based scholarship of discovery that employs an exploratory method involving the scientific approach of experimental mathematics. The mathematical method was used in doing the explorations, focusing on the formulations and proofs of theorems and giving some examples. For the main results, ten theorems were proven and several examples of sequences were provided. The theorems include several formulas for (n(m),k(m))-factoriangular numbers, and (n(a),k(b))-factoriangular numbers. The proofs for theorems in (n(m),k(m))-factoriangular numbers are applicable for similar theorems in (n(a),k(b))-factoriangular numbers. Specific sequences of some generalized factoriangular numbers were presented in tables. Entries of numbers in the tables may lead to the formation of triangular arrays of factoriangular numbers that may be further explored by other researchers, especially those mostly interested in recreational mathematics.

Suggested Citation

  • Romer C. Castillo, 2025. "Mathematical explorations on the sequence of factoriangular numbers: Extending the results on generalizations," Edelweiss Applied Science and Technology, Learning Gate, vol. 9(3), pages 891-904.
    • Handle: RePEc:ajp:edwast:v:9:y:2025:i:3:p:891-904:id:5378
    as

    Download full text from publisher

    File URL: https://learning-gate.com/index.php/2576-8484/article/view/5378/1957
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ajp:edwast:v:9:y:2025:i:3:p:891-904:id:5378. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Melissa Fernandes (email available below). General contact details of provider: https://learning-gate.com/index.php/2576-8484/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.