login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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). 2

%I #27 Jan 28 2019 13:57:52

%S 1,2,2,6,10,32,68,220,528,1724,4460,14664,39908,131944,372448,1237016,

%T 3589384,11967140,35479312,118675768,357957984,1200724776,3673173656,

%U 12351611656,38232022416

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

%C From _Roger Ford_, Oct 12 2015: (Start)

%C a(n)= Number of semi-meander solutions for n with 2 returns to the x axis (or number of 2 distinct arch groups).

%C Example: n=5 -= return to x axis

%C /\ /\ /\

%C //\\ / \ /\ //\\

%C ///\\\ / /\\ /\ //\\ ///\\\

%C /\-////\\\\- /\-//\//\\\- //\\-///\\\- ////\\\\-/\-

%C /\

%C / \ /\

%C //\ \ //\\ /\

%C ///\\/\\-/\- ///\\\-//\\- a(5)=6.

%C a(n)= Number of hills (arches with a peak at 1 and no covering arches) for semi-meander solutions with n-1 arches.

%C Example: n=5 semi-meander solutions with 4 arches (/\)= hill

%C /\ /\

%C /\ /\ //\\ //\\

%C (/\)(/\)//\\ //\\(/\)(/\) ///\\\(/\) (/\)///\\\ a(5)=6.

%C (End)

%C From _Roger Ford_, Jan 27 2018: (Start)

%C 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.)

%C Example: n=5

%C 12354 |3-4| = 1, 14325(1) |2-1| = 1, 12453 |4-3| = 1,

%C 14532 |4-3| = 1, 15234 |1-2| = 1, 13542 |3-4| = 1, a(5)=6.

%C (End)

%H Albert Sade, <a href="/A000108/a000108_17.pdf">Sur les Chevauchements des Permutations</a>, published by the author, Marseille, 1949. [Annotated scanned copy]

%Y Column k=2 of A259689.

%K nonn,more

%O 2,2

%A _N. J. A. Sloane_, Aug 04 2015

%E Corrected and extended by _Roger Ford_, Oct 12 2015

%E a(14)-(26) from _Andrew Howroyd_, Dec 05 2018

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 05:28 EDT 2024. Contains 371264 sequences. (Running on oeis4.)