

A228178


The number of boundary edges for all ordered trees with n edges.


2



1, 4, 14, 47, 157, 529, 1805, 6238, 21812, 77062, 274738, 987276, 3572568, 13007398, 47617798, 175171543, 647227453, 2400843823, 8937670603, 33380986153, 125045165773, 469700405533, 1768752809221, 6676088636479, 25252913322299, 95712549267151, 363441602176007, 1382467779393307, 5267219868722803
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

Apparently partial sums of A071722.  R. J. Mathar, Aug 25 2013


LINKS

Table of n, a(n) for n=0..28.


FORMULA

G.f.: (x*C+2*x^2*C^4)/(1x) where C is the g.f. for the Catalan numbers A000108.
Conjecture: 2*(n+3)*a(n) +2*(7*n11)*a(n1) +(29*n+7)*a(n2) +(21*n+19)*a(n3) +2*(2*n5)*a(n4)=0.  R. J. Mathar, Aug 25 2013


EXAMPLE

The 5 ordered trees with 3 edges have 3,3,2,3,3 boundary edges with UDUDUD having but 2.


PROG

(PARI)
x = 'x + O('x^66);
C = serreverse( x/( 1/(1x) ) ) / x; \\ Catalan A000108
gf = (x*C+2*x^2*C^4)/(1x);
Vec(gf) \\ Joerg Arndt, Aug 21 2013


CROSSREFS

Cf. A000108.
Sequence in context: A289780 A320404 A137284 * A000908 A121095 A264816
Adjacent sequences: A228175 A228176 A228177 * A228179 A228180 A228181


KEYWORD

nonn


AUTHOR

Louis Shapiro, Aug 20 2013


STATUS

approved



