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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 Table of n, a(n) for n=0..20. 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. Cf. A005811, A027336, A066099, A239312, A274174, A351014, A351597, A353849, A353850, A353864, A354905, A354907. Sequence in context: A188223 A348125 A135575 * A355611 A306973 A130114 Adjacent sequences: A354907 A354908 A354909 * A354911 A354912 A354913 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.)