#OEIS #Partitions
https://oeis.org/A334442
https://oeis.org/A334439
How should integer partitions be listed in the OEIS, what offset should the sequences have, and how should the empty partition be handled?
As an example, let's consider A334439: Irregular triangle whose rows are all integer partitions of n sorted first by sum, then by length, ...
This sequence can also be interpreted as the following triangle, whose n-th row is itself a finite triangle with A000041(n) rows.
0
(1)
(2)(11)
(3)(21)(111)
(4)(31)(22)(211)(1111)
(5)(41)(32)(311)(221)(2111)(11111)
The apex of this triangle is the empty partition, which, however, does not appear in the sequence as it is represented in the OEIS.
1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 4, 3, ..
Probably therefore the index was set to 1. However, this is disputed; the original author had set it to 0. Which value do you consider correct? The same applies to A334301 and A334302.
And then there's also A334442: Irregular triangle whose reversed rows are all integer partitions sorted first by sum, then by length, ...
This sequence can also be interpreted as the following triangle:
0
(1)
(2)(11)
(3)(12)(111)
(4)(13)(22)(112)(1111)
(5)(14)(23)(113)(122)(1112)(11111)
Listed as: 1, 2, 1, 1, 3, 1, 2, 1, 1, .
Here, the offset has been set to 0! Do you see any reason to set it differently in this case than in the other three? Or is it clear to you that A334442 has offset 0, and A334439 has offset 1?
[Q 1] Don't you expect the same offset in all cases?
[Q 2] What offset do you expect? 0 or 1?