A228178 The number of boundary edges for all ordered trees with n edges.

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

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: A320404 A137284 A365987 * A000908 A121095 A264816

Adjacent sequences: A228175 A228176 A228177 * A228179 A228180 A228181

Keyword

nonn

Author

Louis Shapiro, Aug 20 2013

Status

approved