Ken's Puzzle of the Week

Sum Pyramid

    8    
  3   5  
2   1   4

Place unique positive integers into a pyramid such that each number equals the sum of the two numbers below it.  Minimize the top number.  A solution for three rows is above.  Solve for 4, 5, and 6 rows.  (or more...).  To remove reflections in submissions, let the lower left corner be less than the lower right.

Source: Original.  Based on what ought to be a classic puzzle I found in the recent Games Magazine, with 6 rows and the top number of 100.


Solutions were received from Keith F. Lynch, Joseph DeVincentis, Philippe Fondanaiche, Alan O'Donnell, Luis Baztan, Kirk Bresniker, David Madfes, Claudio Baiocchi.  Joe sent a simple summary for 4, 5 and 6 rows:

          98
        46  52
      26  20  32
    17   9  11  21
  12   5   4   7  14
10   2   3   1   6   8

        43
      20  23
    12   8  15
   9   3   5  10
 7   2   1   4   6

The two solutions for a 4-pyramid of 20 can be seen embedded in the above solutions.
 

Most solvers pointed me to several other sites where this has been analyzed:
http://www.research.att.com/~njas/sequences/A028307
http://www.research.att.com/~njas/sequences/a028307.txt
http://www.lacim.uqam.ca/~plouffe/OEIS/txt/a028307.txt
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