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A354910 Number of compositions of n that are the run-sums of some other composition. 3
1, 1, 1, 3, 5, 9, 16, 31, 54, 101, 183, 336, 609, 1121, 2038, 3730, 6804, 12445, 22703, 41501, 75768 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
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).
LINKS
EXAMPLE
The a(0) = 0 through a(6) = 16 compositions:
() (1) (2) (3) (4) (5) (6)
(12) (13) (14) (15)
(21) (22) (23) (24)
(31) (32) (33)
(121) (41) (42)
(122) (51)
(131) (123)
(212) (132)
(221) (141)
(213)
(222)
(231)
(312)
(321)
(1212)
(2121)
MATHEMATICA
Table[Length[Union[Total/@Split[#]&/@ Join@@Permutations/@IntegerPartitions[n]]], {n, 0, 15}]
CROSSREFS
The version for binary words is A000126, complement A000918
The complement is counted by A354909, ranked by A354904.
These compositions are ranked by A354912 = nonzeros of A354578.
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: A188223 A348125 A135575 * A355611 A306973 A130114
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 20 2022
STATUS
approved

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Last modified June 15 03:12 EDT 2024. Contains 373402 sequences. (Running on oeis4.)