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 A078629 #9 Mar 31 2012 10:29:01 %S A078629 1,6,100,4244,311424,34883924,5552752356 %N A078629 Number of ways to lace a shoe that has n pairs of eyelets, assuming the lacing satisfies certain conditions. %C A078629 The lace must follow a Hamiltonian path through the 2n eyelets and cannot pass in order though three adjacent eyelets that are in a line. %C A078629 The lace is "directed": reversing the order of eyelets along the path counts as a different solution (cf. A078674). %H A078629 N. J. A. Sloane, <a href="/A078629/a078629.txt">FORTRAN program</a> %H A078629 <a href="/index/La#lacings">Index entries for sequences related to shoe lacings</a> %e A078629 Label the eyelets 1, ..., n from front to back on the left and from n+1, ..., 2n from back to front on the right. For n=2 all 6 lacings are allowed: 1 2 3 4, 2 1 3 4, 3 1 2 4, 1 3 2 4, 2 3 1 4, 3 2 1 4. %e A078629 a(3) = 100: the first few lacings are: 4 2 1 3 5 6, 2 4 1 3 5 6, 1 4 2 3 5 6, 2 1 4 3 5 6, 1 2 4 3 5 6, 1 3 4 2 5 6, 3 1 4 2 5 6, 4 1 3 2 5 6, 1 4 3 2 5 6, 3 4 1 2 5 6, 4 3 1 2 5 6, 3 4 2 1 5 6, 2 4 3 1 5 6, ... %Y A078629 See A078601 and A078602 for other ways of counting lacings. Cf. A078674. %K A078629 nonn,more %O A078629 1,2 %A A078629 _N. J. A. Sloane_, Dec 12 2002 %E A078629 a(7) from _Hugo Pfoertner_, Jan 22 2005