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A374699
Number of integer compositions of n whose leaders of maximal anti-runs are not weakly decreasing.
4
0, 0, 0, 0, 0, 1, 2, 5, 14, 34, 78, 180, 407, 907, 2000, 4364, 9448, 20323, 43448, 92400, 195604, 412355, 866085, 1813035, 3783895, 7875552
OFFSET
0,7
COMMENTS
The leaders of maximal 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.
EXAMPLE
The a(0) = 0 through a(8) = 14 compositions:
. . . . . (122) (1122) (133) (233)
(1221) (1222) (1133)
(11122) (1223)
(11221) (1322)
(12211) (1331)
(11222)
(12122)
(12212)
(12221)
(21122)
(111122)
(111221)
(112211)
(122111)
MATHEMATICA
Table[Length[Select[Join@@Permutations /@ IntegerPartitions[n], !GreaterEqual@@First/@Split[#, UnsameQ]&]], {n, 0, 15}]
CROSSREFS
The complement is counted by A374682.
Other types of runs (instead of anti-):
- For leaders of identical runs we have A056823.
- For leaders of weakly increasing runs we have A374636, complement A189076?
- For leaders of strictly increasing runs: A375135, complement A374697.
Other types of run-leaders (instead of weakly decreasing):
- For identical leaders we have A374640, ranks A374520, complement A374517, ranks A374519.
- For distinct leaders we have A374678, ranks A374639, complement A374518, ranks A374638.
- For weakly increasing leaders we have complement A374681.
- For strictly increasing leaders we have complement complement A374679.
- For strictly decreasing leaders we have complement A374680.
A003242 counts anti-runs, ranks A333489.
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.
A274174 counts contiguous compositions, ranks A374249.
A333381 counts maximal anti-runs in standard compositions.
Sequence in context: A018015 A080039 A344236 * A265226 A357835 A369591
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 06 2024
STATUS
approved