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www.mikescher.com/www/statics/euler/Euler_Problem-045_description.md

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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.