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A339575
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.
2
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
OFFSET
1,2
COMMENTS
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
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..10011 (rows for n = 1..141, flattened)
EXAMPLE
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;
...
From Omar E. Pol, Jan 19 2022: (Start)
For n = 10 the Dyck path described in the 10th row of A237593 is as shown below in the fourth quadrant:
.
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
.
.
-y
.
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)
PROG
(PARI) See Links section.
CROSSREFS
Row sums are A024916.
Sequence in context: A253900 A327487 A105496 * A167618 A211707 A303363
KEYWORD
nonn,tabl,look
AUTHOR
N. J. A. Sloane, Dec 11 2020
EXTENSIONS
Name edited by Omar E. Pol, Jan 22 2022
STATUS
approved