Tetrahedral number

http://en.wikipedia.org/wiki/Tetrahedral_number

http://oeis.org/A000292

0, 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 364, 455, 560, 680, 816, 969, 1140, 1330, 1540, 1771, 2024, 2300, 2600, 2925, 3276, 3654, 4060, 4495, 4960, 5456, 5984, 6545, 7140, 7770, 8436, 9139, 9880, 10660, 11480, 12341, 13244, 14190, 15180

A.J. Meyl proved in 1878 that only three tetrahedral numbers are also perfect squares, namely:
T1 = 1^2 = 1
T2 = 2^2 = 4
T48 = 140^2 = 19600.

The only tetrahedral number that is also a square pyramidal number is 1 (Beukers, 1988), and the only tetrahedral number that is also a perfect cube is 1.