From Roger Ford, Oct 12 2015: (Start)
a(n)= Number of semimeander solutions for n with 2 returns to the x axis (or number of 2 distinct arch groups).
Example: n=5 = return to x axis
/\ /\ /\
//\\ / \ /\ //\\
///\\\ / /\\ /\ //\\ ///\\\
/\////\\\\ /\//\//\\\ //\\///\\\ ////\\\\/\
/\
/ \ /\
//\ \ //\\ /\
///\\/\\/\ ///\\\//\\ a(5)=6.
a(n)= Number of hills (arches with a peak at 1 and no covering arches) for semimeander solutions with n1 arches.
Example: n=5 semimeander solutions with 4 arches (/\)= hill
/\ /\
/\ /\ //\\ //\\
(/\)(/\)//\\ //\\(/\)(/\) ///\\\(/\) (/\)///\\\ a(5)=6.
(End)
From Roger Ford, Jan 27 2018: (Start)
a(n)= Number of solutions for folding a strip of n stamps with stamp 1 on top and each solution ordering having the absolute value of the difference of the stamp number before and after stamp n equal to 1. (If stamp n is the last stamp in the solution ordering then add a(1) to the end of the ordering.)
Example: n=5
12354 34 = 1, 14325(1) 21 = 1, 12453 43 = 1,
14532 43 = 1, 15234 12 = 1, 13542 34 = 1, a(5)=6.
(End)
