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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)/(1-x) where C is the g.f. for the Catalan numbers A000108.

Conjecture: 2*(n+3)*a(n) +2*(-7*n-11)*a(n-1) +(29*n+7)*a(n-2) +(-21*n+19)*a(n-3) +2*(2*n-5)*a(n-4)=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/(1-x) ) ) / x; \\ Catalan A000108

gf = (x*C+2*x^2*C^4)/(1-x);

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

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Last modified December 13 01:23 EST 2019. Contains 329963 sequences. (Running on oeis4.)