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A352832
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Number of reversed integer partitions y of n with exactly one fixed point y(i) = i.
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12
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0, 1, 1, 1, 4, 3, 7, 7, 14, 19, 24, 32, 46, 60, 85, 109, 140, 179, 239, 300, 397, 495, 636, 790, 995, 1239, 1547, 1926, 2396, 2942, 3643, 4432, 5435, 6602, 8038, 9752, 11842, 14292, 17261, 20714, 24884, 29733, 35576, 42375, 50522, 60061, 71363, 84551, 100101
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OFFSET
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0,5
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COMMENTS
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A reversed integer partition of n is a finite weakly increasing sequence of positive integers summing to n.
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LINKS
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EXAMPLE
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The a(0) = 0 through a(8) = 14 partitions (empty column indicated by dot):
. (1) (11) (111) (13) (14) (15) (16) (17)
(22) (1112) (114) (115) (116)
(112) (11111) (222) (1123) (134)
(1111) (1113) (11113) (224)
(1122) (11122) (233)
(11112) (111112) (1115)
(111111) (1111111) (2222)
(11114)
(11123)
(11222)
(111113)
(111122)
(1111112)
(11111111)
For example, the reversed partition (2,2,4) has a unique fixed point at the second position.
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MATHEMATICA
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pq[y_]:=Length[Select[Range[Length[y]], #==y[[#]]&]];
Table[Length[Select[Reverse/@IntegerPartitions[n], pq[#]==1&]], {n, 0, 30}]
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CROSSREFS
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* = unproved
These partitions are ranked by A352831.
A352822 counts fixed points of prime indices.
A352833 counts partitions by fixed points.
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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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