Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:

Triangle		$T_n=n(n+1)/2$		$1,3,6,10,15,\dots$
Pentagonal		$P_n=n(3n-1)/2$		$1,5,12,22,35,\dots$
Hexagonal		$H_n=n(2n-1)$		$1,6,15,28,45,\dots$

It can be verified that $T_{285}=P_{165}=H_{143}=40755$.

Find the next triangle number that is also pentagonal and hexagonal.