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!)
A143362 Triangle read by rows: T(n,k) is the number of ordered trees with n edges and k protected vertices (0<=k<=n-1). A protected vertex in an ordered tree is a vertex at least 2 edges away from its leaf descendants. 2
1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 17, 13, 10, 1, 1, 43, 50, 22, 15, 1, 1, 123, 141, 109, 33, 21, 1, 1, 343, 481, 325, 205, 46, 28, 1, 1, 1004, 1491, 1286, 631, 351, 61, 36, 1, 1, 2938, 4929, 4280, 2861, 1101, 562, 78, 45, 1, 1, 8791, 15840, 15662, 10025, 5676, 1783, 855, 97 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
Row sums are the Catalan numbers (A000108).
Sum(k*T(n,k),k>=0) = A014301(n).
T(n,0) = A143363(n)
LINKS
Gi-Sang Cheon and Louis W. Shapiro, Protected points in ordered trees, Appl. Math. Letters, 21, 2008, 516-520.
FORMULA
G.f.: G-1, where G=G(t,z) satisfies G = 1/(1-zG) + z(t-1)(G-1)/(1+z-zG).
EXAMPLE
T(3,2)=1 because among the five ordered trees with 3 edges only the path tree has 2 vertices at least two edges away from the leaf.
Triangle starts:
1;
1,1;
3,1,1;
6,6,1,1;
17,13,10,1,1;
43,50,22,15,1,1;
MAPLE
eq:=G-1/(1-z*G)-z*(t-1)*(G-1)/(1+z-z*G): G:=RootOf(eq, G): Gser:=simplify(series(G-1, z=0, 13)): for n to 11 do P[n]:=sort(expand(coeff(Gser, z, n))) end do: for n to 11 do seq(coeff(P[n], t, j), j=0..n-1) end do; # yields sequence in triangular form
CROSSREFS
Sequence in context: A146769 A189610 A172427 * A182823 A210866 A245474
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Aug 20 2008
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 June 21 06:38 EDT 2024. Contains 373540 sequences. (Running on oeis4.)