Square triangular 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 to 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