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A375297
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Number of integer compositions of n matching both of the dashed patterns 23-1 and 1-32.
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1
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0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 21, 68, 199, 545, 1410, 3530, 8557, 20255, 46968, 107135, 240927, 535379, 1177435, 2566618, 5551456
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OFFSET
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0,11
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COMMENTS
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Also the number of integer compositions of n whose leaders of maximal weakly increasing runs are not weakly decreasing and whose reverse satisfies the same condition.
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LINKS
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EXAMPLE
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The a(0) = 0 through a(11) = 21 compositions:
. . . . . . . . . (12321) (1342) (1352)
(2431) (2531)
(12421) (11342)
(13231) (12431)
(112321) (12521)
(123211) (13241)
(13421)
(14231)
(23132)
(24311)
(112421)
(113231)
(122321)
(123212)
(123221)
(124211)
(132311)
(212321)
(1112321)
(1123211)
(1232111)
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MATHEMATICA
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Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], MatchQ[#, {___, y_, z_, ___, x_, ___}/; x<y<z]&&MatchQ[#, {___, x_, ___, z_, y_, ___}/; x<y<z]&]], {n, 0, 15}]
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CROSSREFS
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For leaders of identical runs we have A332834.
These compositions are ranked by A375407.
A106356 counts compositions by number of maximal anti-runs.
A335456 counts patterns matched by compositions.
Cf. A000041, A056823, A188920, A189076, A238343, A333213, A335514, A374631, A374632, A374635, A374681.
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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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