## Triangular, pentagonal, and hexagonal

### Problem 45

Published on Friday, 6th June 2003, 06:00 pm; Solved by 33631

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

Triangle |  | Tn=n(n+1)/2 |  | 1, 3, 6, 10, 15, ...
Pentagonal |  | Pn=n(3n1)/2 |  | 1, 5, 12, 22, 35, ...
Hexagonal |  | Hn=n(2n1) |  | 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.