Almost Equilaterial Heronian Triangles An Almost Equilateral Heronian Triangle is a triangle with integer lengths of the form n-1, n, and n+1 and also has integer area. The first few are:

 3,  4,  5 -&gt;    6
13, 14, 15 -&gt;   84
51, 52, 53 -&gt; 1170


Quest: Generate the shortest program that outputs the nth such triple. (Hint: this is a known sequence).

Winner will be selected on May 2, 2014.
Mathematica, 26, 22, 16 18 chars
{0,1,2}+⌊(2+√3)^n⌋