A Maple One-Line Proof of George Andrews's Formula that Says that the Number of Triangles with Integer Sides Whose Perimeter is n Equals {$n^2/12$} -[n/4][(n+2)/4]

TL;DR

This paper presents a concise proof of George Andrews's formula for counting integer-sided triangles with perimeter n, using a finite case-checking approach that is rigorously justified.

Contribution

It offers a one-line Maple proof of Andrews's formula, demonstrating a novel application of finite case verification in a rigorous mathematical proof.

Findings

The formula accurately counts triangles with integer sides and perimeter n.

Finite case checking suffices for rigorous proof in this context.

The Maple proof simplifies the verification process.

Abstract

Yet another example where "physical" (i.e. only checking finitely many special cases) gives a fully rigorous proof, notwithstanding what your "Intro To Proofs" prof told you!