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 A071706 #9 Aug 04 2024 20:32:58
%S A071706 1,1,3,5,21,69,319,1957,12513,85445,656771,5591277,51531405,509874417,
%T A071706 5438826975,62000480093,752464463029,9685138399785,131777883431119
%N A071706 Number of complete mappings f(x) of the cyclic group Z_{2n+1} such that -f(-x)=f.
%C A071706 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.
%C A071706 a(n) is the number of complete mappings fixed under rotation R180 where R180(f)(x)=-f(-x). This sequence (n) equals TSQ_R180(n), the number of solutions of the toroidal n-queen problem fixed under rotation R180. A solution of toroidal-semi n-queen problem is a permutation f(x) of Zn such that f(x)-x is also a permutation.
%D A071706 Y. P. Shieh, "Partition strategies for #P-complete problems with applications to enumerative combinatorics", PhD thesis, National Taiwan University, 2001.
%D A071706 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.
%H A071706 Y. P. Shieh, <a href="http://turing.csie.ntu.edu.tw/~arping/cm">Cyclic complete mappings counting problems</a>
%e A071706 f(x)=6x in (Z7,+) is a complete mapping of Z7 since f(0)=0 and f(x)-x (=5x) is also a permutation of Z7. R180(f)(x)=-f(-x) (=6x). So f(x) is fixed under R180.
%K A071706 nonn
%O A071706 0,3
%A A071706 J. Hsiang, D. F. Hsu and Y. P. Shieh (arping(AT)turing.csie.ntu.edu.tw), Jun 03 2002
%E A071706 Offset corrected by _Sean A. Irvine_, Aug 04 2024