Arrange the numbers from 1 to 15 in such an order that any two consecutive numbers in the sequence add up to a perfect square.

I have got two solutions and I think that these solutions are unique:

The arrangements are as follows:

9,7,2,14,11,5,4,12,13,3,6,10,15,1,8

8,1,15,10,6,3,13,12,4,5,11,14,2,7,9

This problem could have been also written as:

Arrange the numbers from 1 to 17 in such an order that any two consecutive numbers in the sequence add up to a perfect square.

In this case the arrangement would have been:

16,9,7,2,14,11,5,4,12,13,3,6,10,15,1,8,17

17,8,1,15,10,6,3,13,12,4,5,11,14,2,7,9,16