This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A006204 M2802 #39 Aug 05 2024 13:52:36
%S A006204 1,1,3,9,25,133,631,3857,25905,188181,1515283,13376125,128102625,
%T A006204 1317606101,14534145947,170922533545,2138089212789
%N A006204 Number of starters in cyclic group of order 2n+1.
%C A006204 A complete mapping of a cyclic group (Z_m,+) is a permutation f(x) of Z_m with f(0)=0 such that f(x)-x is also a permutation. a(n) is the number of complete mappings f(x) of the cyclic group Z_{2n+1} such that f^(-1)=f.
%C A006204 In other words, a(n) is the number of complete mappings fixed under the reflection operator R, where R(f)=f^(-1). Reflection R is not only a symmetry operator of complete mappings, but also one of the (Toroidal)-(semi) N-Queen problems and of the strong complete mappings problem.
%D A006204 CRC Handbook of Combinatorial Designs, 1996, p. 469.
%D A006204 CRC Handbook of Combinatorial Designs, 2nd edition, 2007, p. 624.
%D A006204 J. D. Horton, Orthogonal starters in finite Abelian groups, Discrete Math., 79 (1989/1990), 265-278.
%D A006204 V. Linja-aho and Patric R. J. Östergård, Classification of starters, J. Combin. Math. Combin. Comput. 75 (2010), 153-159.
%D A006204 Y. P. Shieh, "Partition strategies for #P-complete problems with applications to enumerative combinatorics", PhD thesis, National Taiwan University, 2001.
%D A006204 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.
%D A006204 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006204 Bill Butler, <a href="http://www.durangobill.com/BridgeCyclicSolutions.html">Durango Bill's Bridge Probabilities and Combinatorics</a>
%H A006204 Jieh Hsiang, Yuhpyng Shieh, Yaochiang Chen, <a href="https://www.researchgate.net/publication/2568740_The_Cyclic_Complete_Mappings_Counting_Problems">Cyclic complete mappings counting problems</a>, National Taiwan University, Taipei, April 2003.
%H A006204 Vesa Linja-aho, Patric R. J. Östergård, <a href="http://citeseerx.ist.psu.edu/pdf/bd21ec620182693b5f3629abbe7dbcd987f2d16f">Classification of starters</a>, J. Combin. Math. Combin. Comput. 75 (2010), 153-159.
%e A006204 f(x)=6x in (Z_7,+) is a complete mapping of Z_7 since f(0)=0 and f(x)-x (=5x) is also a permutation of Z_7. f^(-1)(x)=6x=f(x). So f(x) is fixed under reflection.
%Y A006204 Cf. A006717, A071607, A071608, A071706, A003111.
%K A006204 nonn,nice,hard,more
%O A006204 1,3
%A A006204 _N. J. A. Sloane_
%E A006204 Additional comments and one more term from J. Hsiang, D. F. Hsu and Y. P. Shieh (arping(AT)turing.csie.ntu.edu.tw), Jun 03 2002
%E A006204 Corrected and extended by _Roland Bacher_, Dec 18 2007
%E A006204 Extended by Vesa Linja-aho (vesa.linja-aho(AT)tkk.fi), May 06 2009