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A354909
Number of integer compositions of n that are not the run-sums of any other composition.
3
0, 0, 1, 1, 3, 7, 16, 33, 74, 155, 329, 688, 1439, 2975, 6154, 12654, 25964, 53091, 108369, 220643, 448520
OFFSET
0,5
COMMENTS
Every sequence can be uniquely split into a sequence of non-overlapping runs. For example, the runs of (2,2,1,1,1,3,2,2) are ((2,2),(1,1,1),(3),(2,2)), with sums (4,3,3,4).
EXAMPLE
The a(0) = 0 through a(6) = 16 compositions:
. . (11) (111) (112) (113) (114)
(211) (311) (411)
(1111) (1112) (1113)
(1121) (1122)
(1211) (1131)
(2111) (1221)
(11111) (1311)
(2112)
(2211)
(3111)
(11112)
(11121)
(11211)
(12111)
(21111)
(111111)
MATHEMATICA
Table[Length[Complement[Join@@Permutations/@IntegerPartitions[n], Total/@Split[#]&/@Join@@Permutations/@IntegerPartitions[n]]], {n, 0, 15}]
CROSSREFS
The version for binary words is A000918, complement A000126.
These compositions are ranked by A354904 = positions of zeros in A354578.
The complement is counted by A354910, ranked by A354912.
A003242 counts anti-run compositions, ranked by A333489.
A238279 and A333755 count compositions by number of runs.
A353851 counts compositions with all equal run-sums, ranked by A353848.
A353853-A353859 pertain to composition run-sum trajectory.
A353932 lists run-sums of standard compositions, rows ranked by A353847.
Sequence in context: A217942 A002936 A014668 * A182615 A181893 A054455
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 19 2022
STATUS
approved