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 A336132 Number of ways to split a strict integer partition of n into contiguous subsequences all having different sums. 13
 1, 1, 1, 3, 3, 5, 8, 11, 14, 21, 30, 37, 51, 66, 86, 120, 146, 186, 243, 303, 378, 495, 601, 752, 927, 1150, 1395, 1741, 2114, 2571, 3134, 3788, 4541, 5527, 6583, 7917, 9511, 11319, 13448, 16040, 18996, 22455, 26589, 31317, 36844, 43518, 50917, 59655, 69933 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Table of n, a(n) for n=0..48. Gus Wiseman, Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict. EXAMPLE The a(1) = 1 through a(7) = 14 splits: (1) (2) (3) (4) (5) (6) (7) (2,1) (3,1) (3,2) (4,2) (4,3) (2),(1) (3),(1) (4,1) (5,1) (5,2) (3),(2) (3,2,1) (6,1) (4),(1) (4),(2) (4,2,1) (5),(1) (4),(3) (3,2),(1) (5),(2) (3),(2),(1) (6),(1) (4),(2,1) (4,2),(1) (4),(2),(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, Select[IntegerPartitions[n], UnsameQ@@#&]}], {n, 0, 30}] CROSSREFS The version with equal instead of different sums is A318683. Starting with a composition gives A336127. Starting with a strict composition gives A336128. Starting with a partition gives A336131. 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: A285069 A262736 A318684 * A200737 A200741 A271970 Adjacent sequences: A336129 A336130 A336131 * A336133 A336134 A336135 KEYWORD nonn AUTHOR Gus Wiseman, Jul 11 2020 STATUS approved

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Last modified June 2 13:38 EDT 2023. Contains 363097 sequences. (Running on oeis4.)