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A353391
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Number of compositions of n that are empty, a singleton, or whose run-lengths are a subsequence that is already counted.
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11
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1, 1, 1, 1, 2, 1, 3, 1, 1, 4, 5, 7, 9, 11, 15, 22, 38, 45, 87, 93
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OFFSET
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0,5
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LINKS
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EXAMPLE
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The a(9) = 4 through a(14) = 15 compositions (A..E = 10..14):
(9) (A) (B) (C) (D) (E)
(333) (2233) (141122) (2244) (161122) (2255)
(121122) (3322) (221123) (4422) (221125) (5522)
(221121) (131122) (221132) (151122) (221134) (171122)
(221131) (221141) (221124) (221143) (221126)
(231122) (221142) (221152) (221135)
(321122) (221151) (221161) (221153)
(241122) (251122) (221162)
(421122) (341122) (221171)
(431122) (261122)
(521122) (351122)
(531122)
(621122)
(122121122)
(221121221)
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MATHEMATICA
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yosQ[y_]:=Length[y]<=1||MemberQ[Subsets[y], Length/@Split[y]]&&yosQ[Length/@Split[y]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], yosQ]], {n, 0, 15}]
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CROSSREFS
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The non-recursive reverse version is A353403.
The consecutive version is A353430.
These compositions are ranked by A353431.
A114901 counts compositions with no runs of length 1.
A325705 counts partitions containing all of their distinct multiplicities.
A329739 counts compositions with all distinct run-length.
Cf. A005811, A032020, A103295, A114640, A165413, A181591, A242882, A324572, A325702, A333755, A351013, A353401.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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