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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A303284 Number of permutations p of [n] such that the sequence of ascents and descents of 0p or of 0p0 (if n is odd) forms a Dyck path. 5
1, 1, 1, 4, 8, 60, 172, 1974, 7296, 114972, 518324, 10490392, 55717312, 1384890104, 8460090160, 250150900354, 1726791794432, 59317740001132, 456440969661508, 17886770092245360, 151770739970889792, 6687689652133397064, 62022635037246022000, 3037468107154650475868 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..400

Wikipedia, Counting lattice paths

FORMULA

a(2n) = A303287(2n).

EXAMPLE

a(0) = 1: the empty permutation.

a(1) = 1: 1.

a(2) = 1: 21.

a(3) = 4: 132, 213, 231, 312.

a(4) = 8: 1432, 2143, 2431, 3142, 3241, 3421, 4132, 4231.

MAPLE

b:= proc(u, o, t) option remember; `if`(u+o=0, 1,

      `if`(t>0,   add(b(u-j, o+j-1, t-1), j=1..u), 0)+

      `if`(o+u>t, add(b(u+j-1, o-j, t+1), j=1..o), 0))

    end:

a:= n-> b(0, n, 0):

seq(a(n), n=0..25);

MATHEMATICA

b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1, If[t > 0, Sum[b[u - j, o + j - 1, t - 1], {j, 1, u}], 0] + If[o + u > t, Sum[b[u + j - 1, o - j, t + 1], {j, 1, o}], 0]];

a[n_] := b[0, n, 0];

Table[a[n], {n, 0, 25}] (* Jean-François Alcover, May 25 2018, translated from Maple *)

PROG

(PARI) b(u, o, t) = if(u+o==0, 1, if(t > 0, sum(j=1, u, b(u-j, o+j-1, t-1)), 0) + if(o+u > t, sum(j=1, o, b(u+j-1, o-j, t+1)), 0))

a(n) = b(0, n, 0) \\ Felix Fröhlich, May 25 2018, adapted from Mathematica

CROSSREFS

Bisections give: A303285 (even part), A303286 (odd part).

Cf. A180056, A303287.

Sequence in context: A063083 A270399 A269998 * A275574 A214590 A215713

Adjacent sequences:  A303281 A303282 A303283 * A303285 A303286 A303287

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 20 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 May 30 05:08 EDT 2020. Contains 334712 sequences. (Running on oeis4.)