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 A336127 Number of ways to split a composition of n into contiguous subsequences with different sums. 20
 1, 1, 2, 8, 16, 48, 144, 352, 896, 2432, 7168, 16896, 46080, 114688, 303104, 843776, 2080768, 5308416, 13762560, 34865152, 87818240, 241172480, 583008256, 1503657984, 3762290688, 9604956160, 23689428992, 60532195328, 156397207552, 385137770496, 967978254336 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A composition of n is a finite sequence of positive integers summing to n. LINKS Table of n, a(n) for n=0..30. Gus Wiseman, Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict. FORMULA a(n) = Sum_{k=0..n} 2^(n-k) k! A008289(n,k). EXAMPLE The a(0) = 1 through a(4) = 16 splits: () (1) (2) (3) (4) (1,1) (1,2) (1,3) (2,1) (2,2) (1,1,1) (3,1) (1),(2) (1,1,2) (2),(1) (1,2,1) (1),(1,1) (1),(3) (1,1),(1) (2,1,1) (3),(1) (1,1,1,1) (1),(1,2) (1),(2,1) (1,2),(1) (2,1),(1) (1),(1,1,1) (1,1,1),(1) MATHEMATICA splits[dom_]:=Append[Join@@Table[Prepend[#, Take[dom, i]]&/@splits[Drop[dom, i]], {i, Length[dom]-1}], {dom}]; Table[Sum[Length[Select[splits[ctn], UnsameQ@@Total/@#&]], {ctn, Join@@Permutations/@IntegerPartitions[n]}], {n, 0, 10}] CROSSREFS The version with equal instead of different sums is A074854. Starting with a strict composition gives A336128. Starting with a partition gives A336131. Starting with a strict partition gives A336132 Partitions of partitions are A001970. Partitions of compositions are A075900. Compositions of compositions are A133494. Compositions of partitions are A323583. Cf. A006951, A063834, A279786, A305551, A316245, A317715, A323433, A336130, A336134, A336135. Sequence in context: A134353 A280229 A360323 * A076508 A162584 A100243 Adjacent sequences: A336124 A336125 A336126 * A336128 A336129 A336130 KEYWORD nonn AUTHOR Gus Wiseman, Jul 09 2020 STATUS approved

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Last modified June 2 15:21 EDT 2023. Contains 363098 sequences. (Running on oeis4.)