Write a function that takes in a list of integers and returns the maximum sum that can be obtained by selecting a contiguous subsequence of the list, subject to the constraint that no two elements in the subsequence can be adjacent in the original list. For example, if the input list is [3, 4, 1, 2, 5], the function should return 9, since the maximum sum can be obtained by selecting the subsequence [3, 1, 5].