

A354910


Number of compositions of n that are the runsums 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
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OFFSET

0,4


COMMENTS

Every sequence can be uniquely split into a sequence of nonoverlapping 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

A353851 counts compositions with all equal runsums, ranked by A353848.
A353932 lists runsums of standard compositions, rows ranked by A353847.
Cf. A005811, A027336, A066099, A239312, A274174, A351014, A351597, A353849, A353850, A353864, A354905, A354907.


KEYWORD

nonn,more


AUTHOR



STATUS

approved



