This problem was given out at the 2008 Santa Clara Valley Mathematics Field Day competition.

A *triangular number, T _{n} = 1+2+3+ ... + n.* There are some triangular numbers which
are the products of three consecutive positive integers.
For example,

It turns out that there are exactly six triangular numbers which are the products of three integers.

Write a program that fills in the following table where TFTN# represents the index of the "Three Factors of Triangular Numbers." Your function should return a list containing six lists of three elements. It should be of the form: ((3 1 6) ... (22736 636 258474216)) where the first number in each triplet is the n in 1+2+...+n, the second number is the FIRST number in x(x+1)(x+2), and the last number is the triangular number.

The Three Factors | Triangular Number | Notation | ||||||

TFTN# | 1st | 2nd | 3rd | |||||
---|---|---|---|---|---|---|---|---|

1 |
1 |
2 |
3 |
Π= |
6 |
= |
T |
3 |

2 |
Π= |
|||||||

3 |
Π= |
|||||||

4 |
Π= |
|||||||

5 |
Π= |
|||||||

6 |
636 |
637 |
638 |
Π= |
258474216 |
= |
T |
22736 |