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A339575
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Triangle read by rows: T(n,k) is the number of cells in the k-th row of the diagram constructed in the fourth quadrant with the Dyck path described in the n-th row of A237593, 1 <= k <= n.
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2
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1, 2, 2, 3, 3, 2, 4, 4, 4, 3, 5, 5, 5, 3, 3, 6, 6, 6, 6, 5, 4, 7, 7, 7, 7, 5, 4, 4, 8, 8, 8, 8, 8, 6, 5, 5, 9, 9, 9, 9, 9, 7, 7, 5, 5, 10, 10, 10, 10, 10, 10, 8, 7, 6, 6, 11, 11, 11, 11, 11, 11, 8, 7, 6, 6, 6, 12, 12, 12, 12, 12, 12, 12, 10, 10, 9, 7, 7
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OFFSET
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1,2
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COMMENTS
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These are the lengths of the rows if one regards the n-th region in the diagram as the Young diagram corresponding to a partition of A024916(n).
Column k gives the partial sums of the k-th column of triangle A240061. - Omar E. Pol, Dec 11 2020
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LINKS
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EXAMPLE
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Triangle begins:
1;
2, 2;
3, 3, 2;
4, 4, 4, 3;
5, 5, 5, 3, 3;
6, 6, 6, 6, 5, 4;
7, 7, 7, 7, 5, 4, 4;
8, 8, 8, 8, 8, 6, 5, 5;
9, 9, 9, 9, 9, 7, 7, 5, 5;
10, 10, 10, 10, 10, 10, 8, 7, 6, 6;
11, 11, 11, 11, 11, 11, 8, 7, 6, 6, 6;
12, 12, 12, 12, 12, 12, 12, 10, 10, 9, 7, 7;
...
For n = 10 the Dyck path described in the 10th row of A237593 is as shown below in the fourth quadrant:
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k 10th row
. . . . . . . . . . . . . X of triangle
1 . | 10
2 . | 10
3 . | 10
4 . | 10
5 . | 10
6 . _ _| 10
7 . _| 8
8 . _| 7
9 . | 6
10 . _ _ _ _ _ _| 6
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-y
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T(10,k) is the number of cells in the k-th row of the diagram.
The total number of cells in all rows of the diagram is equal to A024916(10) = 87, the same as the sum of the 10th row of triangle. (End)
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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