Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:
| Â | Â | Â |
|---|---|---|
| Triangle | Tn=n(n+1)/2 | 1, 3, 6, 10, 15, … |
| Pentagonal | Pn=n(3n-1)/2 | 1, 5, 12, 22, 35, … |
| Hexagonal | Hn=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.
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