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 A336135 Number of ways to split an integer partition of n into contiguous subsequences with strictly decreasing sums. 15
 1, 1, 2, 5, 8, 16, 29, 50, 79, 135, 213, 337, 522, 796, 1191, 1791, 2603, 3799, 5506, 7873, 11154 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..20. EXAMPLE The a(1) = 1 through a(5) = 16 splittings: (1) (2) (3) (4) (5) (1,1) (2,1) (2,2) (3,2) (1,1,1) (3,1) (4,1) (2),(1) (2,1,1) (2,2,1) (1,1),(1) (3),(1) (3,1,1) (1,1,1,1) (3),(2) (2,1),(1) (4),(1) (1,1,1),(1) (2,1,1,1) (2,2),(1) (3),(1,1) (3,1),(1) (1,1,1,1,1) (2,1),(1,1) (2,1,1),(1) (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], Greater@@Total/@#&]], {ctn, IntegerPartitions[n]}], {n, 0, 10}] CROSSREFS The version with equal sums is A317715. The version with strictly increasing sums is A336134. The version with weakly increasing sums is A336136. The version with weakly decreasing sums is A316245. The version with different sums is A336131. Starting with a composition gives A304961. Starting with a strict partition gives A318684. 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, A323433, A336128, A336130, A336133. Sequence in context: A026007 A032233 A026530 * A032254 A323586 A048237 Adjacent sequences: A336132 A336133 A336134 * A336136 A336137 A336138 KEYWORD nonn,more AUTHOR Gus Wiseman, Jul 11 2020 STATUS approved

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Last modified June 6 04:47 EDT 2023. Contains 363139 sequences. (Running on oeis4.)