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A071608
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Number of complete mappings f(x) of Z_{2n+1} such that -(-id+f)^(-1)=f.
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2
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1, 1, 0, 4, 0, 0, 80, 48, 0, 3328, 1920, 0, 270080, 131328, 0, 3257736, 16379904, 0, 5750476800, 2942582784, 0, 1376249266176, 706948005888, 0, 430415593603072
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OFFSET
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0,4
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COMMENTS
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A complete mapping of a cyclic group (Zn,+) is a permutation f(x) of Zn such that f(0)=0 and that f(x)-x is also a permutation.
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REFERENCES
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Y. P. Shieh, "Partition strategies for #P-complete problems with applications to enumerative combinatorics", PhD thesis, National Taiwan University, 2001.
Y. P. Shieh, J. Hsiang and D. F. Hsu, "On the enumeration of Abelian k-complete mappings", vol. 144 of Congressus Numerantium, 2000, pp. 67-88.
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LINKS
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Table of n, a(n) for n=0..24.
Y. P. Shieh, Cyclic complete mappings counting problems
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EXAMPLE
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f(x)=3x in (Z_7,+) is a complete mapping of Z_7 since f(0)=0 and f(x)-x (=2x) is also a permutation of Z_7. And -(-id+f)^(-1)(x)=f(x).
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CROSSREFS
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Sequence in context: A054376 A351156 A358292 * A013451 A013462 A326862
Adjacent sequences: A071605 A071606 A071607 * A071609 A071610 A071611
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KEYWORD
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nonn
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AUTHOR
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J. Hsiang, D. F. Hsu and Y. P. Shieh (arping(AT)turing.csie.ntu.edu.tw), Jun 03 2002
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STATUS
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approved
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