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A365826
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Number of strict integer partitions of n that are not of length 2 and do not contain n/2.
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3
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1, 1, 1, 1, 1, 1, 1, 2, 2, 4, 4, 7, 7, 12, 12, 20, 20, 30, 31, 45, 46, 66, 68, 93, 97, 130, 136, 179, 188, 242, 256, 325, 344, 432, 459, 568, 606, 742, 793, 963, 1031, 1240, 1331, 1589, 1707, 2026, 2179, 2567, 2766, 3240, 3493, 4072, 4393, 5094, 5501, 6351
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OFFSET
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0,8
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COMMENTS
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Also the number of strict integer partitions of n without two parts (allowing parts to be re-used) summing to n.
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LINKS
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EXAMPLE
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The a(6) = 1 through a(12) = 7 strict partitions:
(6) (7) (8) (9) (10) (11) (12)
(4,2,1) (5,2,1) (4,3,2) (6,3,1) (5,4,2) (5,4,3)
(5,3,1) (7,2,1) (6,3,2) (7,3,2)
(6,2,1) (4,3,2,1) (6,4,1) (7,4,1)
(7,3,1) (8,3,1)
(8,2,1) (9,2,1)
(5,3,2,1) (5,4,2,1)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&FreeQ[Total/@Tuples[#, 2], n]&]], {n, 0, 30}]
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CROSSREFS
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The complement is counted by A365659.
A182616 counts partitions of 2n that do not contain n, strict A365828.
Cf. A004526, A005408, A008967, A035363, A058984, A086543, A100959, A344415, A365376, A365377, A365543.
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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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