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A374680
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Number of integer compositions of n whose leaders of anti-runs are strictly decreasing.
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9
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1, 1, 1, 3, 5, 8, 16, 31, 52, 98, 179, 323, 590, 1078, 1945, 3531, 6421, 11621, 21041, 38116, 68904, 124562, 225138, 406513, 733710, 1323803
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OFFSET
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0,4
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COMMENTS
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The leaders of anti-runs in a sequence are obtained by splitting it into maximal consecutive anti-runs (sequences with no adjacent equal terms) and taking the first term of each.
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LINKS
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EXAMPLE
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The a(0) = 1 through a(6) = 16 compositions:
() (1) (2) (3) (4) (5) (6)
(12) (13) (14) (15)
(21) (31) (23) (24)
(121) (32) (42)
(211) (41) (51)
(131) (123)
(212) (132)
(311) (141)
(213)
(231)
(312)
(321)
(411)
(1212)
(2112)
(2121)
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MATHEMATICA
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Table[Length[Select[Join@@Permutations /@ IntegerPartitions[n], Greater@@First/@Split[#, UnsameQ]&]], {n, 0, 15}]
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CROSSREFS
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For distinct but not necessarily decreasing leaders we have A374518.
For partitions instead of compositions we have A375133.
Other types of runs (instead of anti-):
- For leaders of identical runs we have A000041.
- For leaders of weakly increasing runs we have A188920.
- For leaders of weakly decreasing runs we have A374746.
- For leaders of strictly decreasing runs we have A374763.
- For leaders of strictly increasing runs we have A374689.
Other types of run-leaders (instead of strictly decreasing):
- For weakly increasing leaders we have A374681.
- For strictly increasing leaders we have A374679.
- For weakly decreasing leaders we have A374682.
A106356 counts compositions by number of maximal anti-runs.
A238279 counts compositions by number of maximal runs
A238424 counts partitions whose first differences are an anti-run.
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KEYWORD
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nonn,more,new
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AUTHOR
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STATUS
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approved
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