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

If there is 1 child, there can be 0 interactions.

If there are 2 children, there can be 3 interactions.

If there are 3 children, there can be 12 interactions.

If there are 4 children, there can be 39 interactions.

Which recursive equation represents the pattern?

a. a_n= a_{n - 1}+ 3^{(n - 1)}

b. a_n= a_{n - 1}+ 3(n - 1)

c. a_n= a_{n - 1}+ (3n - 1)

d. a_n= a_{n - 1}+ (n - 1)³