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A325354
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Number of reversed integer partitions of n whose k-th differences are weakly increasing for all k.
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11
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1, 1, 2, 3, 5, 6, 10, 11, 15, 19, 24, 25, 36, 37, 43, 54, 63, 64, 80, 81, 100, 113, 122, 123, 151, 166, 178, 195, 217, 218, 269, 270, 295, 316, 332, 372, 424, 425, 447, 472, 547, 550, 616, 617, 659, 750, 777, 782, 862, 885, 995, 1032, 1083, 1090, 1176, 1275
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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) are (-3,-2).
The zeroth differences of a sequence are the sequence itself, while the k-th differences for k > 0 are the differences of the (k-1)-th differences.
The Heinz numbers of these partitions are given by A325400.
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LINKS
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EXAMPLE
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The a(1) = 1 through a(8) = 15 reversed partitions:
(1) (2) (3) (4) (5) (6) (7) (8)
(11) (12) (13) (14) (15) (16) (17)
(111) (22) (23) (24) (25) (26)
(112) (113) (33) (34) (35)
(1111) (1112) (114) (115) (44)
(11111) (123) (124) (116)
(222) (223) (125)
(1113) (1114) (224)
(11112) (11113) (1115)
(111111) (111112) (1124)
(1111111) (2222)
(11114)
(111113)
(1111112)
(11111111)
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MATHEMATICA
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Table[Length[Select[Sort/@IntegerPartitions[n], And@@Table[OrderedQ[Differences[#, k]], {k, 0, Length[#]}]&]], {n, 0, 30}]
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CROSSREFS
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Cf. A007294, A240026, A325353, A325356, A325360, A325362, A325391, A325393, A325394, A325400, A325404, A325406, A325468.
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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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