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A358907
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Number of finite sequences of distinct integer compositions with total sum n.
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8
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1, 1, 2, 8, 18, 54, 156, 412, 1168, 3200, 8848, 24192, 66632, 181912, 495536, 1354880, 3680352, 9997056, 27093216, 73376512, 198355840, 535319168, 1443042688, 3884515008, 10445579840, 28046885824, 75225974912, 201536064896, 539339293824, 1441781213952
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OFFSET
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0,3
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LINKS
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EXAMPLE
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The a(1) = 1 through a(4) = 18 sequences:
((1)) ((2)) ((3)) ((4))
((11)) ((12)) ((13))
((21)) ((22))
((111)) ((31))
((1)(2)) ((112))
((2)(1)) ((121))
((1)(11)) ((211))
((11)(1)) ((1111))
((1)(3))
((3)(1))
((1)(12))
((11)(2))
((1)(21))
((12)(1))
((2)(11))
((21)(1))
((1)(111))
((111)(1))
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MAPLE
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g:= proc(n) option remember; ceil(2^(n-1)) end:
b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0, (t->
add(binomial(t, j)*b(n-i*j, i-1, p+j), j=0..min(t, n/i)))(g(i))))
end:
a:= n-> b(n$2, 0):
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MATHEMATICA
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comps[n_]:=Join@@Permutations/@IntegerPartitions[n];
Table[Length[Select[Join@@Table[Tuples[comps/@c], {c, comps[n]}], UnsameQ@@#&]], {n, 0, 10}]
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CROSSREFS
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This is the strict case of A133494.
The version for sequences of partitions is A358906.
A001970 counts multiset partitions of integer partitions.
A218482 counts sequences of compositions with weakly decreasing lengths.
A358830 counts twice-partitions with distinct lengths.
A358901 counts partitions with all different Omegas.
A358914 counts twice-partitions into distinct strict partitions.
Cf. A000009, A000041, A000219, A055887, A075900, A296122, A304961, A307068, A336342, A358836, A358912.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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