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A353392
Number of compositions of n whose own run-lengths are a consecutive subsequence.
9
1, 1, 0, 0, 1, 2, 2, 2, 2, 8, 12, 16, 20, 35, 46, 59, 81, 109, 144, 202, 282
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 version is A353390, ranked by A353402.
The non-consecutive recursive version is A353391, ranked by A353431.
The non-consecutive reverse version is A353403.
The recursive version is A353430.
These compositions are ranked by A353432.
A003242 counts anti-run compositions, ranked by A333489.
A011782 counts compositions.
A169942 counts Golomb rulers, ranked by A333222.
A325676 counts knapsack compositions, ranked by A333223.
A329738 counts uniform compositions, partitions A047966.
A329739 counts compositions with all distinct run-lengths.
Sequence in context: A152660 A339163 A058787 * A360310 A085056 A371619
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, May 15 2022
STATUS
approved