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)