OFFSET
0,13
COMMENTS
A partition is Look-and-Say iff it has a permutation with all distinct run-lengths. For example, the partition y = (2,2,2,1,1,1) has the permutation (2,2,1,1,1,2), with run-lengths (2,3,1), which are distinct, so y is counted under A239455(9).
A partition is Wilf iff it has distinct multiplicities of parts. For example, (2,2,2,1,1,1) has multiplicities (3,3), so is not counted under A098859(9).
Is a(17) = 0 the last zero of the sequence?
EXAMPLE
The a(9) = 1 through a(18) = 5 partitions are (empty columns not shown):
n=9: n=12: n=15: n=16: n=18:
--------------------------------------------------------------
(222111) (333111) (333222) (33331111) (444222)
(22221111) (444111) (555111)
(2222211111) (3322221111)
(32222211111)
(222222111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], !UnsameQ@@Length/@Split[#]&&Select[Permutations[#], UnsameQ@@Length/@Split[#]&]!={}&]], {n, 0, 15}]
CROSSREFS
A032020 = number of binary expansions with all distinct run-lengths.
A044813 = numbers whose binary expansion has all distinct run-lengths.
A329738 = compositions with all equal run-lengths.
A329739 = compositions with all distinct run-lengths
A351013 = compositions with all distinct runs.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Feb 16 2022
STATUS
approved