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A365827
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Number of strict integer partitions of n whose length is not 2.
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5
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1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 6, 7, 10, 12, 16, 20, 25, 30, 38, 45, 55, 66, 79, 93, 111, 130, 153, 179, 209, 242, 282, 325, 375, 432, 496, 568, 651, 742, 846, 963, 1094, 1240, 1406, 1589, 1795, 2026, 2282, 2567, 2887, 3240, 3634, 4072, 4557, 5094, 5692, 6351
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OFFSET
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0,7
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COMMENTS
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Also the number of strict integer partitions of n with no pair of distinct parts summing to n.
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LINKS
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FORMULA
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EXAMPLE
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The a(5) = 1 through a(13) = 12 strict partitions (A..D = 10..13):
(5) (6) (7) (8) (9) (A) (B) (C) (D)
(321) (421) (431) (432) (532) (542) (543) (643)
(521) (531) (541) (632) (642) (652)
(621) (631) (641) (651) (742)
(721) (731) (732) (751)
(4321) (821) (741) (832)
(5321) (831) (841)
(921) (931)
(5421) (A21)
(6321) (5431)
(6421)
(7321)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Length[#]!=2&]], {n, 0, 30}]
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CROSSREFS
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The complement is counted by A140106 shifted left.
A046663 counts partitions with no submultiset summing to k, strict A365663.
A182616 counts partitions of 2n that do not contain n, strict A365828.
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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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