OFFSET
0,6
COMMENTS
The row length sequence of this table is p(n)=A000041(n) (number of partitions).
In order to count distinct parts of a partition consider the partition as a set instead of a multiset. E.g., n=6: read [3,1,1,1] as {1,3} and count the elements, here 2.
Rows are the same as the rows of A103921, but in reverse order.
LINKS
Robert Price, Table of n, a(n) for n = 0..9295 (25 rows).
FORMULA
a(n, m) = number of distinct parts of the m-th partition of n in Mathematica order; n >= 0, m = 1..p(n) = A000041(n).
EXAMPLE
Triangle starts:
0
1
1, 1
1, 2, 1
1, 2, 1, 2, 1
1, 2, 2, 2, 2, 2, 1
1, 2, 2, 2, 1, 3, 2, 1, 2, 2, 1
1, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 1
1, 2, 2, 2, 2, 3, 2, 1, 3, 2, 3, 2, 2, 2, 3, 3, 2, 1, 2, 2, 2, 1
1, 2, 2, 2, 2, 3, 2, 2, ...
a(5,4)=2 from the fourth partition of 5 in the mentioned order, i.e., [3,1^2], which has two distinct parts, namely 1 and 3.
MATHEMATICA
Table[Length /@ Union /@ IntegerPartitions[n], {n, 0, 8}] // Flatten (* Robert Price, Jun 11 2020 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Franklin T. Adams-Watters, Jan 25 2006
EXTENSIONS
Edited and corrected by Franklin T. Adams-Watters, May 29 2006
STATUS
approved