A Maple One-Liner that Proves George Andrews’s Theorem That The Number of Triangles with Integer Sides Whose Perimeter is n equals \{\frac{n^{2}}{12} \} − ⌊\frac{n}{4}⌋⌊\frac{n+2}{4}⌋

Shalosh B. EKHAD ^{1}

evalb(seq(coeff(taylor(q**3/(1-q**2)/(1-q**3)/(1-q**4),q=0,37),q,i),i=0..36)
=seq(round(n**2/12)-trunc(n/4)*trunc((n+2)/4),n=0..36));

1 c/o zeilberg at math dot rutgers dot edu.

Exclusively published in: http://www.math.rutgers.edu/~zeilberg/pj.html . Feb. 4 2012.