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Factor Triangle

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  • Kermit Rose
    Factor Triangle 0 1 0 4 3 0 9 8 5 0 16 15 12 7 0 25 24 21 16 9 0 36 35 32 27 20 11 To construct the triangle:
    Message 1 of 1 , Jun 3, 2009
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      Factor Triangle

      0
      1 0
      4 3 0
      9 8 5 0
      16 15 12 7 0
      25 24 21 16 9 0
      36 35 32 27 20 11

      To construct the triangle:

      Sequence number the rows, starting with zero.
      Sequence number the columns, starting with zero.

      Column zero is the square of row number.
      In row t, cell (t,s) = cell(t,s-1) - cell(s,s-1)

      cell(2,1) = cell(2,0) - cell(1,0) ; 3 = 4 - 1
      cell(2,2) = cell(2,1) - cell(2,1) ; 0 = 3 - 3
      cell(3,1) = cell(3,0) - cell(1,0) ; 8 = 9 - 1
      cell(3,2) = cell(3,1) - cell(2,1) ; 5 = 8 - 3
      etc

      Study of the internal properties of this triangle might
      or might not be of use for deriving factor algorithms.

      An example of an internal property:



      0
      1 0
      4 3 0
      9 8 5 0
      16 15 12 7 0
      25 24 21 16 9 0
      36 35 32 27 20 11


      35 = 35 + 0 = 32 + 3 = 27 + 8 = 20 + 15 = 11 + 24

      32 = 32 + 0 = 27 + 5 = 20 + 12 = 11 + 21

      27 = 27 + 0 = 20 + 7 = 11 + 16

      20 = 20 + 0 = 11 + 0

      cell(t,s) = cell(t,b) + cell(b,s) for s < b < t.

      Kermit
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