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A325324
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Number of integer partitions of n whose differences (with the last part taken to be 0) are distinct.
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18
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1, 1, 2, 1, 3, 4, 4, 7, 7, 7, 10, 15, 13, 22, 25, 26, 31, 43, 39, 55, 54, 68, 75, 98, 97, 128, 135, 165, 177, 217, 223, 277, 282, 339, 356, 438, 444, 527, 553, 667, 694, 816, 868, 1015, 1054, 1279, 1304, 1538, 1631, 1849, 1958, 2304, 2360, 2701, 2899, 3267
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OFFSET
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0,3
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COMMENTS
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The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (6,3,1) (with the last part taken to be 0) are (-3,-2,-1).
The Heinz numbers of these partitions are given by A325367.
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LINKS
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EXAMPLE
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The a(1) = 1 through a(11) = 15 partitions (A = 10, B = 11):
(1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B)
(11) (22) (32) (33) (43) (44) (54) (55) (65)
(31) (41) (51) (52) (53) (72) (64) (74)
(311) (411) (61) (62) (81) (73) (83)
(322) (71) (441) (82) (92)
(331) (332) (522) (91) (A1)
(511) (611) (711) (433) (443)
(622) (533)
(631) (551)
(811) (632)
(641)
(722)
(731)
(911)
(6311)
For example, (6,3,1,1) has differences (-3,-2,0,-1), which are distinct, so (6,3,1,1) is counted under a(11).
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], UnsameQ@@Differences[Append[#, 0]]&]], {n, 0, 30}]
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CROSSREFS
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Cf. A007862, A049988, A098859, A130091, A240026, A320348, A320466, A320509, A325325, A325349, A325366, A325367, A325368, A325404, A325407.
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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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