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 only 1 interaction. If there are 3 children, there can be 4 interactions. If there are 4 children, there can be 9 interactions. How many interactions will there be for 8 children?

Question

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 only 1 interaction.  If there are 3 children, there can be 4 interactions.  If there are 4 children, there can be 9 interactions.   How many interactions will there be for 8 children?

directrix · Answer

Let a(1) = 0
a(2) = a(1) + 1 = 0 + 1 = 1

a(3) = a(2) + 3 = 1 + 3 = 4
a(4) = a(3) + 5 = 4 + 5 = 9

a(5) = a(4) + 7 = 9 + 7 = 16

Continue the pattern through a(8).

@wilkin412