How to select a subset from an array so that the sum of the elements of the subset is maximum ?

But there is one interesting condition : -

1)When I select any particular element, I am forced to select the next and previous element as well.

What will be the recurrence-relation/dynamic-programming approach to solve this problem?

Example:- [-10,1,2,3,-5,-6,7,8,9]

We select ‘2’ and ‘8’ and our final answer is, hence :- [1+2+3] + [7+8+9] = 30

Say [1,2,3,4,5]…

If you select ‘2’ and ‘4’, answer will be= 1+2+3+4+5

I have formed a recurrence relation but not very sure about it…

This problem has been created by me , btw…

Update :- I finally discovered a solution on my own .