%I #18 Oct 07 2024 09:08:21
%S 3,45,1824,109560,9520560,1145057760,181091917440
%N Number of ways to lace a shoe with n eyelet pairs such that there is no direct "horizontal" connection between any adjacent eyelet pair.
%C The lacing must not have any "straight connections" between adjacent eyelet pairs (e.g. 2<->2*n-1, 3<->2*n-2, 4<->2*n-3,....). There are no symmetric solutions.
%C From _Sean A. Irvine_, Oct 06 2024: (Start)
%C The lacing must begin and end with the top eyelet pair (1 and 2n in Pfoertner's numbering).
%C Every eyelet must be used.
%C Under versus over crossings are not considered distinct.
%C Three consecutive eyelets on the same side are not permitted.
%C Because there are no symmetric solutions, mirrored solutions can be handled by simply dividing the total solutions by 2. (End)
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a072/A072503.java">Java program</a> (github)
%H Hugo Pfoertner, <a href="http://www.randomwalk.de/shoelace/nonstra.txt">FORTRAN program to count non-straight shoe lacings and results for N=3,4</a>
%H <a href="/index/La#lacings">Index entries for sequences related to shoe lacings</a>
%e The 6 non-straight lacings for n=3 are: 124536, 135426, 142356, 145326, 153246, 154236. Not counting mirror images we get a(3)=3.
%o (Fortran) See Links.
%Y Cf. A078602, A078698, A078702, A002866.
%K nonn,more
%O 3,1
%A _Hugo Pfoertner_, Jan 27 2003
%E a(9) from _Sean A. Irvine_, Oct 07 2024