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A350839
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Number of integer partitions of n with a difference < -1 and a conjugate difference < -1.
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16
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0, 0, 0, 0, 0, 1, 2, 3, 7, 11, 17, 26, 39, 54, 81, 108, 148, 201, 269, 353, 467, 601, 779, 995, 1272, 1605, 2029, 2538, 3171, 3941, 4881, 6012, 7405, 9058, 11077, 13478, 16373, 19817, 23953, 28850, 34692, 41599, 49802, 59461, 70905, 84321, 100155, 118694
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OFFSET
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0,7
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COMMENTS
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We define a difference of a partition to be a difference of two adjacent parts.
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LINKS
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EXAMPLE
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The a(5) = 1 through a(10) = 17 partitions:
(311) (411) (511) (422) (522) (622)
(3111) (4111) (611) (711) (811)
(31111) (3311) (4221) (4222)
(4211) (4311) (4411)
(5111) (5211) (5221)
(41111) (6111) (5311)
(311111) (33111) (6211)
(42111) (7111)
(51111) (42211)
(411111) (43111)
(3111111) (52111)
(61111)
(331111)
(421111)
(511111)
(4111111)
(31111111)
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MATHEMATICA
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conj[y_]:=If[Length[y]==0, y, Table[Length[Select[y, #>=k&]], {k, 1, Max[y]}]];
Table[Length[Select[IntegerPartitions[n], (Min@@Differences[#]<-1)&&(Min@@Differences[conj[#]]<-1)&]], {n, 0, 30}]
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CROSSREFS
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Allowing -1 gives A144300 = non-constant partitions.
These partitions are ranked by A350841.
A277103 = partitions with the same number of odd parts as their conjugate.
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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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