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 A072503 #18 Oct 07 2024 09:08:21 %S A072503 3,45,1824,109560,9520560,1145057760,181091917440 %N A072503 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 A072503 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 A072503 From _Sean A. Irvine_, Oct 06 2024: (Start) %C A072503 The lacing must begin and end with the top eyelet pair (1 and 2n in Pfoertner's numbering). %C A072503 Every eyelet must be used. %C A072503 Under versus over crossings are not considered distinct. %C A072503 Three consecutive eyelets on the same side are not permitted. %C A072503 Because there are no symmetric solutions, mirrored solutions can be handled by simply dividing the total solutions by 2. (End) %H A072503 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a072/A072503.java">Java program</a> (github) %H A072503 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 A072503 <a href="/index/La#lacings">Index entries for sequences related to shoe lacings</a> %e A072503 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 A072503 (Fortran) See Links. %Y A072503 Cf. A078602, A078698, A078702, A002866. %K A072503 nonn,more %O A072503 3,1 %A A072503 _Hugo Pfoertner_, Jan 27 2003 %E A072503 a(9) from _Sean A. Irvine_, Oct 07 2024