A particle moves in the Cartesian Plane according to the following rules:
From any lattice point \((a,b),\) the particle may only move to \((a+1,b), (a,b+1),\) or \((a+1,b+1).\)
There are no right angle turns in the particle's path.
How many different paths can the particle take from \((0,0)\) to \((5,5)\)?
(第二十三届AIME1 2005 第13题)