OFFSET
2,2
COMMENTS
From Roger Ford, Oct 12 2015: (Start)
a(n)= Number of semi-meander 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 semi-meander solutions with n-1 arches.
Example: n=5 semi-meander 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 |3-4| = 1, 14325(1) |2-1| = 1, 12453 |4-3| = 1,
14532 |4-3| = 1, 15234 |1-2| = 1, 13542 |3-4| = 1, a(5)=6.
(End)
LINKS
Albert Sade, Sur les Chevauchements des Permutations, published by the author, Marseille, 1949. [Annotated scanned copy]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, Aug 04 2015
EXTENSIONS
Corrected and extended by Roger Ford, Oct 12 2015
a(14)-(26) from Andrew Howroyd, Dec 05 2018
STATUS
approved