Problem 45
Triangular, pentagonal, and hexagonal
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(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.
三角形数、五边形数和六角形数
三角形数、五边形数和六角形数分别由以下公式给出：
| 三角形数 | Tn=n(n+1)/2 | 1, 3, 6, 10, 15, … |
| 五边形数 | Pn=n(3n−1)/2 | 1, 5, 12, 22, 35, … |
| 六边形数 | Hn=n(2n−1) | 1, 6, 15, 28, 45, … |
可以验证，T285 = P165 = H143 = 40755。
找出下一个同时是三角形数、五边形数和六角形数的数。