login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A259701 Triangle read by rows: T(n,k) = number of permutations without overlaps in which the first increasing run has length k and the second element is not 2. 2
0, 1, 0, 2, 0, 0, 5, 0, 1, 0, 12, 0, 2, 0, 0, 33, 1, 7, 0, 1, 0, 87, 2, 17, 0, 2, 0, 0, 252, 11, 55, 2, 9, 0, 1, 0, 703, 26, 145, 4, 22, 0, 2, 0, 0, 2105, 109, 467, 27, 81, 3, 11, 0, 1, 0, 6099, 280, 1296, 63, 215, 6, 27, 0, 2, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,4

COMMENTS

The 12th row of the triangle given in the Sade reference is incorrect, since the first column of this triangle is known (it is A000560).

REFERENCES

A. Sade, Sur les Chevauchements des Permutations, published by the author, Marseille, 1949

LINKS

Table of n, a(n) for n=2..67.

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

EXAMPLE

Triangle begins:

     0;

     1,   0;

     2,   0,   0;

     5,   0,   1,   0;

    12,   0,   2,   0,  0;

    33,   1,   7,   0,  1, 0;

    87,   2,  17,   0,  2, 0,  0;

   252,  11,  55,   2,  9, 0,  1, 0;

   703,  26, 145,   4, 22, 0,  2, 0, 0;

  2105, 109, 467,  27, 81, 3, 11, 0, 1, 0;

  ...

PROG

(PARI)

Overlapfree(v)={for(i=1, #v, for(j=i+1, v[i]-1, if(v[j]>v[i], return(0)))); 1}

Chords(u)={my(n=2*#u, v=vector(n), s=u[#u]); if(s%2==0, s=n+1-s); for(i=1, #u, my(t=n+1-s); s=u[i]; if(s%2==0, s=n+1-s); v[s]=t; v[t]=s); v}

FirstRunLen(v)={my(e=1); for(i=1, #v, if(v[i]==e, e++)); e-2}

row(n)={my(r=vector(n-1)); if(n>=2, forperm(n, v, if(v[1]<>1, break); if(v[2]<>2 && Overlapfree(Chords(v)), r[FirstRunLen(v)]++))); r}

for(n=2, 8, print(row(n))) \\ Andrew Howroyd, Dec 07 2018

CROSSREFS

Row sums excluding the first column give A259702.

First column is A000560.

Cf. A259703.

Sequence in context: A289088 A057611 A329959 * A147843 A094597 A202992

Adjacent sequences:  A259698 A259699 A259700 * A259702 A259703 A259704

KEYWORD

nonn,tabl,more

AUTHOR

N. J. A. Sloane, Jul 05 2015

EXTENSIONS

a(49) corrected and a(57)-a(67) from Andrew Howroyd, Dec 07 2018

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 3 18:19 EST 2021. Contains 349467 sequences. (Running on oeis4.)