Maximum subsequence sum

Given a sequence of positive numbers, find the maximum sum that can be formed which has no three consecutive elements present.

Examples :

Input: arr[] = {1, 2, 3}

Output: 5

We can't take three of them, so answer is

2 + 3 = 5

Input: arr[] = {3000, 2000, 1000, 3, 10}

Output: 5013

3000 + 2000 + 3 + 10 = 5013

Input: arr[] = {100, 1000, 100, 1000, 1}

Output: 2101

100 + 1000 + 1000 + 1 = 2101

Input: arr[] = {1, 1, 1, 1, 1}

Output: 4

Input: arr[] = {1, 2, 3, 4, 5, 6, 7, 8}

Output: 27