Can you please write a recursive formula for the sequence 03

Can you please write a recursive formula for the sequence 0,3,8,15,24... and explain how you got it?
thank you!

We could see that each number is 1 less than a perfect square.
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1st term: 1^2-1
2nd term: 2^2-1
3rd term: 3^2-1

4th term: 4^2-1

5th term: 5^2-1

Hence the for the recursive function

we have the first term as A(1) = 0

An = A(n-1) + (2n - 1 ) , this is the recursive function where n > 1

lets check

A2 = A(2-1) + (2*2-1) = A(1) + 3 = 0+3 = 3

A3 = A(3-1) + (3*2-1) = A(2) + 5 = 3+5 = 8

A4 = A(4-1) + (4*2-1) = A(3) + (7) = 8 + 7 = 15

A5 = A(5-1) + (5*2-1) = A(4) + (9) = 15 + 9 - 24