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A333149
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Number of strict compositions of n that are neither increasing nor decreasing.
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7
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0, 0, 0, 0, 0, 0, 4, 4, 8, 12, 38, 42, 72, 98, 150, 298, 372, 542, 760, 1070, 1428, 2600, 3120, 4550, 6050, 8478, 10976, 15220, 23872, 29950, 41276, 55062, 74096, 97148, 129786, 167256, 256070, 314454, 429338, 556364, 749266, 955746, 1275016, 1618054
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OFFSET
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0,7
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COMMENTS
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A composition of n is a finite sequence of positive integers summing to n. It is strict if there are no repeated parts.
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LINKS
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FORMULA
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EXAMPLE
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The a(6) = 4 through a(9) = 12 compositions:
(1,3,2) (1,4,2) (1,4,3) (1,5,3)
(2,1,3) (2,1,4) (1,5,2) (1,6,2)
(2,3,1) (2,4,1) (2,1,5) (2,1,6)
(3,1,2) (4,1,2) (2,5,1) (2,4,3)
(3,1,4) (2,6,1)
(3,4,1) (3,1,5)
(4,1,3) (3,2,4)
(5,1,2) (3,4,2)
(3,5,1)
(4,2,3)
(5,1,3)
(6,1,2)
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MATHEMATICA
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Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@#&&!Greater@@#&&!Less@@#&]], {n, 0, 10}]
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CROSSREFS
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The complement is counted by A333147.
Non-unimodal strict compositions are A072707.
Strict partitions with increasing or decreasing run-lengths are A333190.
Strict compositions with increasing or decreasing run-lengths are A333191.
Cf. A059204, A115981, A227038, A329398, A332745, A332746, A332831, A332833, A332835, A332874, A333150, A333192.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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