login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A288115 Number of Dyck paths of semilength n such that each level has exactly eight peaks or no peaks. 2
1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 8, 29, 71, 148, 302, 596, 1101, 1915, 3485, 8991, 32879, 131942, 595068, 2731434, 11077722, 38438377, 117144042, 324706536, 842734665, 2087025088, 4995608093, 11799404719, 28899101722, 79974175125, 268545121874, 1071998634063 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Wikipedia, Counting lattice paths

MAPLE

b:= proc(n, k, j) option remember; `if`(n=j, 1, add(

      b(n-j, k, i)*(binomial(j-1, i-1)+binomial(i, k)

       *binomial(j-1, i-1-k)), i=1..min(j+k, n-j)))

    end:

a:= n-> `if`(n=0, 1, b(n, 8$2)):

seq(a(n), n=0..37);

MATHEMATICA

b[n_, k_, j_] := b[n, k, j] = If[n == j, 1, Sum[b[n - j, k, i]*(Binomial[j - 1, i - 1] + Binomial[i, k]*Binomial[j - 1, i - 1 - k]), {i, 1, Min[j + k, n - j]}]];

a[n_] := If[n == 0, 1, b[n, 8, 8]];

Table[a[n], {n, 0, 37}] (* Jean-Fran├žois Alcover, Jun 02 2018, from Maple *)

CROSSREFS

Column k=8 of A288108.

Sequence in context: A093809 A244244 A037157 * A100178 A106113 A299260

Adjacent sequences:  A288112 A288113 A288114 * A288116 A288117 A288118

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 05 2017

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 April 25 16:59 EDT 2019. Contains 322461 sequences. (Running on oeis4.)