sum of consecutive triangular numbers is a square

[Max Alekseyev]

SeqFan,

Is anybody interested in extending and/or submitting the following sequences?

The numbers k such that there exist k consecutive triangular numbers
whose sum is a square:

1, 2, 3, 4, 11, 13, 22, 23, 25, 27, 32, 37, 39, 46, 47, 48, 49, 50,
52, 59, 66, 71

The numbers k such that there exist unique k consecutive triangular
numbers whose sum is a square:

32, 50

The starting indices of the triangular numbers in the sums above:

26, 26

The square root of the sums above:

172, 265

Max