# Project Euler Problem 45: Triangular, pentagonal, and hexagonal

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

Triangle

$$T_n = \frac{n(n+1)}{2} \\ 1, 3, 6, 10, 15, \dotsc$$Pentagonal

$$P_n = \frac{n(3n−1)}{2} \\ 1, 5, 12, 22, 35, \dotsc$$Hexagonal

$$H_n = n(2n−1) \\ 1, 6, 15, 28, 45, \dotsc$$It can be verified that $T_{285} = P_{165} = H_{143} = 40755$.

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