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A325269
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Number of integer partitions of n with 2 distinct parts or at least 3 parts.
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1
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0, 0, 0, 2, 3, 6, 9, 14, 20, 29, 40, 55, 75, 100, 133, 175, 229, 296, 383, 489, 625, 791, 1000, 1254, 1573, 1957, 2434, 3009, 3716, 4564, 5602, 6841, 8347, 10142, 12308, 14882, 17975, 21636, 26013, 31184, 37336, 44582, 53172, 63260, 75173, 89133, 105556
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OFFSET
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0,4
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COMMENTS
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The Heinz numbers of these partitions are given by A080257.
Partitions with 2 distinct parts are in A002133(n). Partitions with at least 3 parts are in A004250(n). Some partitions are in both subsets, so A002133(n)+A004250(n) >= a(n). - R. J. Mathar, Dec 13 2022
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LINKS
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FORMULA
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EXAMPLE
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The a(1) = 1 through a(8) = 20 partitions:
(21) (31) (32) (42) (43) (53)
(111) (211) (41) (51) (52) (62)
(1111) (221) (222) (61) (71)
(311) (321) (322) (332)
(2111) (411) (331) (422)
(11111) (2211) (421) (431)
(3111) (511) (521)
(21111) (2221) (611)
(111111) (3211) (2222)
(4111) (3221)
(22111) (3311)
(31111) (4211)
(211111) (5111)
(1111111) (22211)
(32111)
(41111)
(221111)
(311111)
(2111111)
(11111111)
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MAPLE
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local a, p, s ;
a := 0 ;
for p in combinat[partition](n) do
s := convert(p, set) ;
if nops(p) >= 3 or nops(s) = 2 then
a := a+1 ;
end if;
end do:
a ;
end proc:
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], Length[Union[#]]==2||Length[#]>2&]], {n, 0, 30}]
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CROSSREFS
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Cf. A001221, A001222, A001358, A001399, A007774, A008284, A060687, A080257, A090858, A116608, A325244.
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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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