Journal of Integer Sequences, Vol. 28 (2025), Article 25.7.7

A Generalized Hockey Stick Theorem


Molly Lynch
Department of Mathematics, Statistics, and Computer Science
Hollins University
7916 Williamson Rd
Roanoke, VA 24020
USA

Michael Weselcouch
School of Health, Science, and Sustainability
221 College Ln
Roanoke College
Salem, VA 24153
USA

Abstract:

We present a combinatorial proof, based on a sign-reversing involution, of a new identity that extends the classical "hockey stick" identity for binomial coefficients.

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(Concerned with sequences A000027 A000217 A000292 A000332 A000389 A000579 A006134 A007318 A057552 A079309 A087413 A188675 A225612 A225615 A263134 A371963 A371964 A371965.)

Received June 19 2025; revised versions received June 20 2025; July 4 2025; October 9 2025; October 31 2025. Published in Journal of Integer Sequences, December 9 2025.

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