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A353430
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Number of integer compositions of n that are empty, a singleton, or whose own run-lengths are a consecutive subsequence that is already counted.
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8
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1, 1, 1, 1, 2, 1, 3, 1, 1, 4, 5, 7, 9, 11, 15, 16, 22, 25, 37, 37, 45
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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(n) compositions for selected n (A..E = 10..14):
n=4: n=6: n=9: n=10: n=12: n=14:
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(4) (6) (9) (A) (C) (E)
(22) (1122) (333) (2233) (2244) (2255)
(2211) (121122) (3322) (4422) (5522)
(221121) (131122) (151122) (171122)
(221131) (221124) (221126)
(221142) (221135)
(221151) (221153)
(241122) (221162)
(421122) (221171)
(261122)
(351122)
(531122)
(621122)
(122121122)
(221121221)
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MATHEMATICA
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yoyQ[y_]:=Length[y]<=1||MemberQ[Join@@Table[Take[y, {i, j}], {i, Length[y]}, {j, i, Length[y]}], Length/@Split[y]]&&yoyQ[Length/@Split[y]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], yoyQ]], {n, 0, 15}]
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CROSSREFS
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A114901 counts compositions with no runs of length 1.
A329739 counts compositions with all distinct run-lengths.
Cf. A005811, A032020, A103295, A114640, A165413, A242882, A325705, A333755, A351013, A353400, 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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