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]
  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! 
Shalosh B. Ekhad
math.CO