## Factor Triangle

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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:
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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