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A352828
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Number of strict integer partitions y of n with no fixed points y(i) = i.
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15
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1, 0, 1, 2, 2, 2, 2, 3, 4, 6, 8, 10, 12, 14, 16, 19, 22, 26, 32, 38, 46, 56, 66, 78, 92, 106, 123, 142, 162, 186, 214, 244, 280, 322, 368, 422, 484, 552, 630, 718, 815, 924, 1046, 1180, 1330, 1498, 1682, 1888, 2118, 2372, 2656, 2972, 3322, 3712, 4146, 4626
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OFFSET
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0,4
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LINKS
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FORMULA
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G.f.: Sum_{n>=0} q^(n*(3*n+1)/2)*Product_{k=1..n}(1+q^k)/(1-q^k). - Jeremy Lovejoy, Sep 26 2022
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EXAMPLE
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The a(0) = 1 through a(12) = 12 partitions (A-C = 10..12; empty column indicated by dot; 0 is the empty partition):
0 . 2 3 4 5 6 7 8 9 A B C
21 31 41 51 43 53 54 64 65 75
61 71 63 73 74 84
431 81 91 83 93
432 532 A1 B1
531 541 542 642
631 632 651
4321 641 732
731 741
5321 831
5421
6321
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MATHEMATICA
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pq[y_]:=Length[Select[Range[Length[y]], #==y[[#]]&]];
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&pq[#]==0&]], {n, 0, 30}]
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CROSSREFS
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A238352 counts reversed partitions by fixed points, rank statistic A352822.
A352833 counts partitions by fixed points.
Cf. A008292, A064410, A111133, A114088, A118199, A188674, A257990, A352824, A352825, A352830, A352872.
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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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