Square triangular number

For squares of triangular numbers, see squared triangular number.

Square triangular number 36 depicted as a triangular number and as a square number.

In mathematics, a square triangular number (or triangular square number) is a number which is both a triangular number and a square number, in other words, the sum of all integers from $1$ to $n$ has a square root that is an integer. There are infinitely many square triangular numbers; the first few are:

0, 1, 36, 1225, 41616, 1413721, 48024900, 1631432881, 55420693056, 1882672131025 (sequence A001110 in the OEIS)

N A001110	s2 = N A001109	t(t+1)/2 = N A001108
0	0	0
1	1	1
36	6	8
1225	35	49
41616	204	288
1413721	1189	1681
48024900	6930	9800