Sums of Diagonals in Pascal’s Triangle

Authors

  • Jamisen McCrary University of Kentucky
  • Russell May Morehead State University

DOI:

https://doi.org/10.33043/EHQGGV66Dz

Abstract

We analyze sums of entries on diagonals of integer slope in Pascal’s triangle, obtain a recurrence relation that these diagonal sums obey, and compute their generating function. We use the generating function to approximate the exponential growth of the diagonal sums.

Author Biographies

Jamisen McCrary, University of Kentucky

Jamisen McCrary is an undergraduate student at the University of Kentucky, studying mechanical engineering. He was previously a student in the Craft Academy at Morehead State University. His inspiration for the research topic was his prior appreciation for Pascal’s Triangle and finding patterns. Apart from mathematics, Jamisen enjoys listening to music, creating art, working with electronics, programming, 3D modeling, cooking, and deep thinking. His overarching goal in life is to become a professor of engineering at a secondary education institution and build up the next generation of engineers to their fullest potential.

Russell May, Morehead State University

Russell May teaches math at Morehead State University and coaches the problem-solving club for the Craft Academy, a dual-credit academy for talented high school students in Kentucky. He is interested in combinatorics, especially problems with nice generating function solutions.

References

Green, Thomas M. Recurrent Sequences and Pascal’s Triangle. Mathematics Magazine, 41(1), 13-21, (1968). http://www.jstor.org/stable/2687953

Joseph A. Raab. A Generalization of the Connection Between the Fibonacci Sequence and Pascal’s Triangle. The Fibonacci Quarterly, 3(3), 21-31, (1963) https://www.fq.math.ca/Scanned/1-3/raab.pdf

Herbert S. Wilf. Generatingfunctionology. A K Peters/CRC Press, (2005).

Paul J. Karafiol et al. American Regions Math League Power & Local Contests 2009–2014. ARML, (2015).

N. J. A. Sloane. Online Encyclopedia of Integer Sequences. http://oeis.org/A000045

N. J. A. Sloane. Online Encyclopedia of Integer Sequences. http://oeis.org/A000045

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Published

2026-03-03

How to Cite

McCrary, J., & May, R. (2026). Sums of Diagonals in Pascal’s Triangle. Mathematics Exchange, 16(1), 50–57. https://doi.org/10.33043/EHQGGV66Dz

Issue

Vol. 16 No. 1 (2022): Mathematics Exchange, Fall 2022

Section

Articles

License

Copyright (c) 2026 Jamisen McCrary, Russell May

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.