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EXAMPLE
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The number of terms in row n is C(n,[n/2]).
Triangle begins:
[1],
[2],
[3,1],
[4,2,2],
[5,3,3,3,1,1],
[6,4,4,4,4,2,2,2,2,2],
[7,5,5,5,5,5,3,3,3,3,3,3,3,3,3,1,1,1,1,1],
[8,6,6,6,6,6,6,4,4,4,4,4,4,4,4,4,4,4,4,4,4,2,2,2,2,2,2,2,2,2,2,2,2,2,2],
[9,7,7,7,7,7,7,7,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
...
ILLUSTRATION OF GENERATING METHOD.
Row n is derived from the binomial coefficients in the following way.
Place markers in an array so that the number of contiguous markers
in row k is C(n,k) and then count the markers along columns.
For example, row 6 of this triangle is generated from C(6,k) like so:
------------------------------------------
1: o - - - - - - - - - - - - - - - - - - -
6: o o o o o o - - - - - - - - - - - - - -
15:o o o o o o o o o o o o o o o - - - - -
20:o o o o o o o o o o o o o o o o o o o o
15:o o o o o o o o o o o o o o o - - - - -
6: o o o o o o - - - - - - - - - - - - - -
1: o - - - - - - - - - - - - - - - - - - -
------------------------------------------
Counting the markers along the columns gives row 6 of this triangle:
[7,5,5,5,5,5,3,3,3,3,3,3,3,3,3,1,1,1,1,1].
Continuing in this way generates all the rows of this triangle.
...
Number of repeated terms in each row of this triangle forms A008315:
1;
1;
1, 1;
1, 2;
1, 3, 2;
1, 4, 5;
1, 5, 9, 5;
1, 6, 14, 14;
1, 7, 20, 28, 14;...
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