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

 Name       | Formula              | Numbers
------------|----------------------|-------------------------
Triangle    | `T_{n} = n(n+1)/2`   | `1, 3, 6, 10, 15, ...`
Pentagonal  | `P_{n} = n(3n-1)/2`  | `1, 5, 12, 22, 35, ...`
Hexagonal   | `H_{n} = n(2n-1)`    | `1, 6, 15, 28, 45, ...`

It can be verified that `T285 = P165 = H143 = 40755`.

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