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A374682
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Number of integer compositions of n whose leaders of anti-runs are weakly decreasing.
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11
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1, 1, 2, 4, 8, 15, 30, 59, 114, 222, 434, 844, 1641, 3189, 6192, 12020, 23320, 45213, 87624, 169744, 328684, 636221, 1231067, 2381269, 4604713, 8901664
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OFFSET
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0,3
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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(5) = 15 compositions:
() (1) (2) (3) (4) (5)
(11) (12) (13) (14)
(21) (22) (23)
(111) (31) (32)
(112) (41)
(121) (113)
(211) (131)
(1111) (212)
(221)
(311)
(1112)
(1121)
(1211)
(2111)
(11111)
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MATHEMATICA
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Table[Length[Select[Join@@Permutations /@ IntegerPartitions[n], GreaterEqual@@First/@Split[#, UnsameQ]&]], {n, 0, 15}]
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CROSSREFS
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For reversed partitions instead of compositions we have A115029.
Other types of runs (instead of anti-):
- For leaders of identical runs we have A000041.
- For leaders of weakly increasing runs we have A189076, complement A374636.
- For leaders of weakly decreasing runs we have A374747.
- For leaders of strictly decreasing runs we have A374765.
- For leaders of strictly increasing runs we have A374697.
Other types of run-leaders (instead of weakly decreasing):
- For weakly increasing leaders we have A374681.
- For strictly increasing leaders we have A374679.
- For strictly decreasing leaders we have A374680.
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
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AUTHOR
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STATUS
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approved
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