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A337698
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Number of compositions of n that are not strictly increasing.
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1
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0, 0, 1, 2, 6, 13, 28, 59, 122, 248, 502, 1012, 2033, 4078, 8170, 16357, 32736, 65498, 131026, 262090, 524224, 1048500, 2097063, 4194200, 8388486, 16777074, 33554267, 67108672, 134217506, 268435200, 536870616, 1073741484, 2147483258, 4294966848, 8589934080
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = 2^(n-1) - A000009(n) for n > 0.
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EXAMPLE
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The a(2) = 1 through a(5) = 13 compositions:
(11) (21) (22) (32)
(111) (31) (41)
(112) (113)
(121) (122)
(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], !Less@@#&]], {n, 0, 15}]
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CROSSREFS
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A140106 counts the unordered case of length 3.
A242771 counts the case of length 3.
A333255 is the complement of a ranking sequence (using standard compositions A066099) for these compositions.
A337481 counts these compositions that are not strictly decreasing.
A337482 counts these compositions that are not weakly decreasing.
A218004 counts strictly increasing or weakly decreasing compositions.
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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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