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A325769
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Number of integer partitions of n whose distinct consecutive subsequences have different sums.
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14
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1, 1, 2, 3, 4, 6, 7, 11, 12, 17, 19, 29, 28, 41, 42, 62, 61, 88, 87, 123, 121, 168, 164, 234, 225, 306, 306, 411, 401, 527, 533, 700, 689, 894, 885, 1163, 1150, 1452, 1469, 1866, 1835, 2333, 2346, 2913, 2913, 3638, 3619, 4511, 4537, 5497, 5576, 6859, 6827, 8263
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OFFSET
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0,3
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COMMENTS
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For example (3,3,1,1) is counted under a(8) because it has distinct consecutive subsequences (), (1), (1,1), (3), (3,1), (3,1,1), (3,3), (3,3,1), (3,3,1,1), all of which have different sums.
The Heinz numbers of these partitions are given by A325778.
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LINKS
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EXAMPLE
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The a(1) = 1 through a(8) = 12 partitions:
(1) (2) (3) (4) (5) (6) (7) (8)
(11) (21) (22) (32) (33) (43) (44)
(111) (31) (41) (42) (52) (53)
(1111) (221) (51) (61) (62)
(311) (222) (322) (71)
(11111) (411) (331) (332)
(111111) (421) (521)
(511) (611)
(2221) (2222)
(4111) (3311)
(1111111) (5111)
(11111111)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], UnsameQ@@Total/@Union[ReplaceList[#, {___, s__, ___}:>{s}]]&]], {n, 0, 30}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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