Search: id:A006717
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%I A006717 M3005
%S A006717 1,3,15,133,2025,37851,1030367,36362925,1606008513,87656896891,5778121715415,
%T A006717 452794797220965,41609568918940625
%N A006717 Toroidal semi-queens on a (2n+1) X (2n+1) board.
%C A006717 Also the number of transversals of a cyclic latin square of order 2n+1 
               and the number of orthomorphisms of the cyclic group of order 2n+1. 
               - Ian M. Wanless (wanless(AT)maths.ox.ac.uk), Oct 07 2001
%C A006717 Also the number of complete mappings of a cyclic group of order 2n+1; 
               also (2n+1) times the number of "standard" complete mappings of cyclic 
               group of order 2n+1. - Jieh Hsiang, D.Frank Hsu and Yuh Pyng Shieh 
               (arping(AT)turing.csie.ntu.edu.tw), May 08 2002
%C A006717 See A003111 for further information.
%D A006717 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006717 B. D. McKay, J. C. McLeod and I. M. Wanless, The number of transversals 
               in a Latin square, Des. Codes Cryptogr., 40, (2006) 269-284.
%D A006717 D. Novakovic, (2000) Computation of the number of complete mappings for 
               permutations. Cybernetics & System Analysis, No. 2, v. 36, pp. 244-247.
%D A006717 Yuh Pyng Shieh, Jieh Hsiang and D. Frank Hsu, On the enumeration of Abelian 
               k-complete mappings, vol. 144 of Congressus Numerantium, 2000, pp. 
               67-88
%D A006717 Yuh Pyng Shieh, Partition Strategies for #P-complete problem with applications 
               to enumerative combinatorics, PhD thesis, National Taiwan University, 
               2001
%D A006717 I. Vardi, Computational Recreations in Mathematica. Addison-Wesley, Redwood 
               City, CA, 1991, p. 118.
%H A006717 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               QueensProblem.html">Link to a section of The World of Mathematics.</
               a>
%F A006717 Every term is odd and if n=2 mod 3 then a(n) is divisible by 3. Also 
               a(n) is asymptotically less than 0.62^n n!. [McKay, McLeod, Wanless]
%Y A006717 Sequence in context: A074241 A117694 A108210 this_sequence A059861 A030539 
               A028362
%Y A006717 Adjacent sequences: A006714 A006715 A006716 this_sequence A006718 A006719 
               A006720
%K A006717 nonn,nice
%O A006717 0,2
%A A006717 N. J. A. Sloane (njas(AT)research.att.com).
%E A006717 More terms from Jieh Hsiang, D. Frank Hsu and Yuh Pyng Shieh (arping(AT)turing.csie.ntu.edu.tw), 
               May 08 2002
%E A006717 a(12) added from A003111 by N. J. A. Sloane (njas(AT)research.att.com), 
               Mar 29 2007

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