What is the sequence for 1,1,3,2,4,6,5,25?

Start with the first number of a group of 3 numbers. The second number of the group is the square of the first number. Add 2 to that to get the next number. Then, subtract 1 to arrive at the first number of the next group.
  1  start
  1 = 1^2
  3 = 1 + 2
  2 = 3 - 1 start
  4 = 2^2
  6 = 4 + 2
  5 = 6 - 1 start
  25 = 5^2
  27 = 25 + 2
  26 = 27 - 1 start
  676 = 26^2
  ...