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A363262
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Number of integer compositions of n in which the greatest part appears more than once.
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4
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0, 1, 1, 2, 4, 9, 18, 37, 73, 145, 287, 570, 1134, 2264, 4526, 9061, 18152, 36374, 72884, 146011, 292416, 585422, 1171632, 2344136, 4688821, 9376832, 18749169, 37485358, 74939850, 149813328, 299492966, 598729533, 1196987066, 2393137399, 4784846896, 9567357951
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OFFSET
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1,4
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COMMENTS
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Also the number of multisets of length n covering an initial interval of positive integers with more than one mode.
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LINKS
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EXAMPLE
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The a(2) = 1 through a(6) = 9 compositions:
(11) (111) (22) (122) (33)
(1111) (212) (222)
(221) (1122)
(11111) (1212)
(1221)
(2112)
(2121)
(2211)
(111111)
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MATHEMATICA
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Table[Length[Select[Join@@Permutations /@ IntegerPartitions[n], Count[#, Max@@#]>1&]], {n, 15}]
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CROSSREFS
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For partitions instead of compositions we have A002865.
The complement is counted by A097979 shifted left.
Row sums of columns k > 1 of A238341.
If all parts appear more than once we have A240085, for partitions A007690.
If the greatest part appears exactly twice we have A243737.
A032020 counts strict compositions.
A261982 counts compositions with some part appearing more than once.
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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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