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A333147
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Number of compositions of n that are either strictly increasing or strictly decreasing.
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8
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1, 1, 1, 3, 3, 5, 7, 9, 11, 15, 19, 23, 29, 35, 43, 53, 63, 75, 91, 107, 127, 151, 177, 207, 243, 283, 329, 383, 443, 511, 591, 679, 779, 895, 1023, 1169, 1335, 1519, 1727, 1963, 2225, 2519, 2851, 3219, 3631, 4095, 4607, 5179, 5819, 6527, 7315, 8193, 9163
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OFFSET
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0,4
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COMMENTS
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A composition of n is a finite sequence of positive integers summing to n.
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LINKS
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FORMULA
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EXAMPLE
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The a(1) = 1 through a(9) = 15 compositions:
(1) (2) (3) (4) (5) (6) (7) (8) (9)
(1,2) (1,3) (1,4) (1,5) (1,6) (1,7) (1,8)
(2,1) (3,1) (2,3) (2,4) (2,5) (2,6) (2,7)
(3,2) (4,2) (3,4) (3,5) (3,6)
(4,1) (5,1) (4,3) (5,3) (4,5)
(1,2,3) (5,2) (6,2) (5,4)
(3,2,1) (6,1) (7,1) (6,3)
(1,2,4) (1,2,5) (7,2)
(4,2,1) (1,3,4) (8,1)
(4,3,1) (1,2,6)
(5,2,1) (1,3,5)
(2,3,4)
(4,3,2)
(5,3,1)
(6,2,1)
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MATHEMATICA
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Table[2*PartitionsQ[n]-1, {n, 0, 30}]
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CROSSREFS
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The non-strict version appears to be A329398.
Partitions with incr. or decr. run-lengths are A332745 (strict: A333190).
Compositions with incr. or decr. run-lengths are A332835 (strict: A333191).
Cf. A059204, A072705, A072707, A115981, A332285, A332578, A332746, A332831, A332833, A332874, A333150.
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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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