The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A336128 Number of ways to split a strict composition of n into contiguous subsequences with different sums. 19
 1, 1, 1, 5, 5, 9, 29, 37, 57, 89, 265, 309, 521, 745, 1129, 3005, 3545, 5685, 8201, 12265, 16629, 41369, 48109, 77265, 107645, 160681, 214861, 316913, 644837, 798861, 1207445 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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. EXAMPLE The a(0) = 1 through a(5) = 5 splits: () (1) (2) (3) (4) (5) (12) (13) (14) (21) (31) (23) (1)(2) (1)(3) (32) (2)(1) (3)(1) (41) (1)(4) (2)(3) (3)(2) (4)(1) The a(6) = 29 splits: (6) (1)(5) (1)(2)(3) (15) (2)(4) (1)(3)(2) (24) (4)(2) (2)(1)(3) (42) (5)(1) (2)(3)(1) (51) (1)(23) (3)(1)(2) (123) (1)(32) (3)(2)(1) (132) (13)(2) (213) (2)(13) (231) (2)(31) (312) (23)(1) (321) (31)(2) (32)(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/@Select[IntegerPartitions[n], UnsameQ@@#&]}], {n, 0, 15}] CROSSREFS The version with equal instead of different sums is A336130. Starting with a non-strict composition gives A336127. 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. Set partitions with distinct block-sums are A275780. Compositions of partitions are A323583. Cf. A006951, A063834, A271619, A279375, A305551, A326519, A317508, A318684, A336133, A336134, A336135. Sequence in context: A173322 A097910 A321655 * A049122 A336140 A321660 Adjacent sequences: A336125 A336126 A336127 * A336129 A336130 A336131 KEYWORD nonn,more AUTHOR Gus Wiseman, Jul 10 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 6 05:06 EDT 2023. Contains 363139 sequences. (Running on oeis4.)