Triangular, Pentagonal, and Hexagonal
Problem 45
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.