Solve the recurrence relation
with the initial condition , and verify your solution by induction on n.
Ok ! I got what you meant. It is :
So, now just try to figure out what the first terms of this sequence are.
Try to find and you'll have quite a good idea of what actually the sequence is.
After that, you'll have to prove this. Induction is an easy way to make it.
Solve the recurrence relation: .
and verify your solution by induction on
Crank out the first few terms and you may see a pattern.
We see that the terms of the sequence are squares,
. . not every consecutive square,
. . but squares of certain numbers.
These are the squares of Triangular Numbers, starting with