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!)
A227850 Number of Dyck paths of semilength n*(4*n+1) in which the run length sequence is a permutation of {1,...,4*n}. 3
1, 4, 1248, 5401472, 114070692352, 7593330670240768 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..5.

EXAMPLE

a(1) = 4: UUDUUUDDDD (2134), UUUDUUDDDD (3124), UUUUDDUDDD (4213), UUUUDDDUDD (4312).

MAPLE

h:= proc(n, s) option remember;

       `if`(n>add(sort([s[]], `>`)[i], i=1..(nops(s)+1)/2), 0,

       add(g(n-i, s minus {i}), i=select(x-> x<=n, s)))

    end:

g:= proc(n, s) option remember;

       `if`(s={}, `if`(n=0, 1, 0), add(h(n+i, s minus {i}), i=s))

    end:

a:= n-> g(0, {$1..4*n}):

seq(a(n), n=0..3);

MATHEMATICA

h[n_, s_] := h[n, s] = If[n > Sum[Sort[s, Greater][[i]], {i, 1, (Length[s] + 1)/2}], 0, Sum[g[n - i, s ~Complement~ {i}], {i, Select[s, # <= n&]}] ];

g[n_, s_] := g[n, s] = If[s == {}, If[n == 0, 1, 0], Sum[h[n + i, s  ~Complement~ {i}], {i, s}]];

a[n_] := g[0, Range[4*n]];

Table[a[n], {n, 0, 4}] (* Jean-Fran├žois Alcover, Apr 23 2016, translated from Maple *)

CROSSREFS

Cf. A007742, A060005, A073410, A168238.

Sequence in context: A253168 A160004 A324299 * A079711 A283260 A217601

Adjacent sequences:  A227847 A227848 A227849 * A227851 A227852 A227853

KEYWORD

nonn,more

AUTHOR

David Scambler and Alois P. Heinz, Oct 31 2013

STATUS

approved

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 May 20 01:04 EDT 2022. Contains 353847 sequences. (Running on oeis4.)