A playground is being designed where children can interact with their friends in certain combinations.

Question

If there is 1 child, there can be 0 interactions.
If there are 2 children, there can be 1 interactions.
If there are 3 children, there can be 4 interactions.
If there are 4 children, there can be 9 interactions.
Which recursive equation represents the pattern?

Answer 1

a(1) = 0
a(n+1) = a(n)+(2n-1)

or,

a(n) = (n-1)^2

Answer 2

Thank you

Could it be written as a(n)=a(n-1)+2^n-3

Answer 3

Did you even check out your idea?

a(1) = 0
a(2) = a(1) + 2^2-3 = 0+1 = 1
a(3) = a(2) + 2^3-3 = 1+5 = 6
a(4) = a(3) + 2^4-3 = 6+13 = 19