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A336127
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Number of ways to split a composition of n into contiguous subsequences with different sums.
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20
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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
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OFFSET
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0,3
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COMMENTS
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A composition of n is a finite sequence of positive integers summing to n.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} 2^(n-k) k! A008289(n,k).
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EXAMPLE
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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)
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MATHEMATICA
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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}]
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CROSSREFS
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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.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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