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A360254
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Number of integer partitions of n with more adjacent equal parts than distinct parts.
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17
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0, 0, 0, 1, 1, 1, 3, 4, 7, 10, 12, 18, 28, 36, 52, 68, 92, 119, 161, 204, 269, 355, 452, 571, 738, 921, 1167, 1457, 1829, 2270, 2834, 3483, 4314, 5300, 6502, 7932, 9665, 11735, 14263, 17227, 20807, 25042, 30137, 36099, 43264, 51646, 61608, 73291, 87146, 103296
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OFFSET
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0,7
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COMMENTS
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None of these partitions is strict.
Also the number of integer partitions of n which, after appending 0, have first differences of median 0.
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LINKS
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EXAMPLE
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The a(3) = 1 through a(9) = 10 partitions:
(111) (1111) (11111) (222) (22111) (2222) (333)
(21111) (31111) (22211) (22221)
(111111) (211111) (41111) (33111)
(1111111) (221111) (51111)
(311111) (222111)
(2111111) (411111)
(11111111) (2211111)
(3111111)
(21111111)
(111111111)
For example, the partition y = (4,4,3,1,1,1,1) has 0-appended differences (0,1,2,0,0,0,0), with median 0, so y is counted under a(15).
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], Length[#]>2*Length[Union[#]]&]], {n, 0, 30}]
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CROSSREFS
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The non-prepended version is A237363.
These partitions have ranks A360558.
For any integer median (not just 0) we have A360688.
A008284 counts partitions by number of parts.
A116608 counts partitions by number of distinct parts.
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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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