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

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]