title: Algorithm to find the maximum subsequence of an array of positive numbers . Catch : No adjacent elements allowed
body: <p>For example, given</p>
  
  <pre><code>A = [1,51,3,1,100,199,3], maxSum = 51 + 1 + 199 = 251.
  </code></pre>
  
  <p>clearly <code>max(oddIndexSum,evenIndexSum)</code> does <b>not</b> work.</p>
  
  <p>The main problem I have is that I can't come up with a selection criterion for an element.
  A rejection criterion is trivial given a selection criterion.</p>
  
  <p>The standard maximum sub-sequence algorithm doesn't seem to be applicable here.
  I have tried a dynamic programming approach, but can't come up with that either. 
  The only approach I could come up with was one that used a genetic algorithm.</p>
  
  <p>How would you approach this?</p>