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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
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=2..26.

Albert Sade, Sur les Chevauchements des Permutations, published by the author, Marseille, 1949. [Annotated scanned copy]

CROSSREFS

Column k=2 of A259689.

Sequence in context: A229733 A265987 A076907 * A153897 A103774 A036052

Adjacent sequences:  A260782 A260783 A260784 * A260786 A260787 A260788

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

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Last modified April 8 02:27 EDT 2020. Contains 333312 sequences. (Running on oeis4.)