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)
Rémy Sigrist, PARI program for A339575
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
AUTHOR
N. J. A. Sloane, Dec 11 2020
EXTENSIONS
Name edited by Omar E. Pol, Jan 22 2022
STATUS
approved