Algorithm to find the maximum subsequence of an array of positive numbers . Catch : No adjacent elements allowed

Question

For example, given

A = [1,51,3,1,100,199,3], maxSum = 51 + 1 + 199 = 251.

clearly max(oddIndexSum,evenIndexSum) does not

Answer 1

A recursive answer in strange Prologesque pseudocode:

maxSum([]) = 0
maxSum([x]) = x
maxSum(A) = max(A[0] + maxSum(A[2..n]),
                A[1] + maxSum(A[3..n]))

With appropriate handling of out-of-range indexes.

Edit: This reduces to MarcusQ's nicer answer:

maxSum([]) = 0
maxSum(A) = max(A[0] + maxSum(A[2..n]), maxSum(A[1..n]))

Edit: Here's a version that returns the actual subsequence rather than just its sum. It stretches the limits of my ad hoc pseudo-Prolog-C Chimera, so I'll stop now.

maxSub([]) = []
maxSub(A) = sub1 = [A[0]] + maxSub(A[2..n])
            sub2 = maxSub(A[1..n])
            return sum(sub1) > sum(sub2) ? sub1 : sub2