OFFSET
0,6
EXAMPLE
The a(0) = 0 through a(10) = 12 compositions (empty columns indicated by dots, 0 is the empty composition):
0 1 . . 22 122 1122 11221 21122 333 1333
221 2211 12211 22112 22113 2233
22122 3322
31122 3331
121122 22114
122112 41122
211221 122113
221121 131122
221131
311221
1211221
1221121
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], #=={}||MemberQ[Join@@Table[Take[#, {i, j}], {i, Length[#]}, {j, i, Length[#]}], Length/@Split[#]]&]], {n, 0, 15}]
CROSSREFS
The non-consecutive version for partitions is A325702.
The non-consecutive reverse version is A353403.
The recursive version is A353430.
These compositions are ranked by A353432.
A011782 counts compositions.
A329739 counts compositions with all distinct run-lengths.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, May 15 2022
STATUS
approved