A325545 revision #9
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A325545
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Number of compositions of n with distinct differences.
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55
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1, 1, 2, 3, 7, 13, 17, 34, 59, 105, 166, 279, 442, 730, 1157, 1927, 3045, 4741, 7527, 11667, 18048, 27928, 43334, 65861, 101385, 153404, 232287, 347643, 523721, 780083, 1165331, 1725966, 2561625, 3773838, 5561577, 8151209, 11920717, 17364461, 25269939, 36635775
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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.
The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (3,1,2) are (-2,1).
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LINKS
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EXAMPLE
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The a(1) = 1 through a(6) = 17 compositions:
(1) (2) (3) (4) (5) (6)
(11) (12) (13) (14) (15)
(21) (22) (23) (24)
(31) (32) (33)
(112) (41) (42)
(121) (113) (51)
(211) (122) (114)
(131) (132)
(212) (141)
(221) (213)
(311) (231)
(1121) (312)
(1211) (411)
(1131)
(1221)
(1311)
(2112)
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MATHEMATICA
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Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@Differences[#]&]], {n, 0, 15}]
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CROSSREFS
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Cf. A000079, A000740, A008965, A059966, A070211, A175342, A242882, A325325, A325352, A325546, A325547, A325548, A325551, A325554.
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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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proposed
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