A260785 Leading diagonal of triangle in A259689: a(n)= number of permutations without overlaps that generate exactly 2 permutations without overlaps in a(n+1).

1, 2, 2, 6, 10, 32, 68, 220, 528, 1724, 4460, 14664, 39908, 131944, 372448, 1237016, 3589384, 11967140, 35479312, 118675768, 357957984, 1200724776, 3673173656, 12351611656, 38232022416

Offset: 2

Author

N. J. A. Sloane, Aug 04 2015

Keywords

• nonn
• more

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

Column k=2 of A259689.

Extensions

Corrected and extended by Roger Ford, Oct 12 2015

a(14)-(26) from Andrew Howroyd, Dec 05 2018