login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A228180 The number of single edges on the boundary of ordered trees with n edges. 2
0, 1, 2, 6, 19, 61, 199, 661, 2234, 7668, 26674, 93858, 333524, 1195288, 4315468, 15681838, 57312643, 210529213, 776872243, 2878482523, 10704933793, 39945106573, 149511432793, 561182969173, 2111812422871, 7965992783803, 30114859723751, 114079902339303, 432975153092011, 1646215731143667 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Apparently the partial sums of A070031. - R. J. Mathar, Aug 25 2013

REFERENCES

D. E. Davenport, L. K. Pudwell, L. W. Shapiro, L. C. Woodson, The Boundary of Ordered Trees, 2014; http://faculty.valpo.edu/lpudwell/papers/treeboundary.pdf

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Dennis E. Davenport, Lara K. Pudwell, Louis W. Shapiro, Leon C. Woodson, The Boundary of Ordered Trees, Journal of Integer Sequences, Vol. 18 (2015), Article 15.5.8.

W. Kuszmaul, Fast Algorithms for Finding Pattern Avoiders and Counting Pattern Occurrences in Permutations, arXiv preprint arXiv:1509.08216, 2015

FORMULA

G.f.: (x*C+2*x^3*C^4)/(1-x) where C is the g.f. for the Catalan numbers A000108.

Conjecture: 2*(n+1)*a(n) +(-13*n+5)*a(n-1) +(23*n-37)*a(n-2) +6*(-2*n+5)*a(n-3)=0. - R. J. Mathar, Aug 25 2013

a(n) ~ 5*4^n / (3*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Feb 01 2014

EXAMPLE

For n=3 the UUUDDD has 3 single edges while UUDDUD, UDUUDD and UUDUDD each have one single edge, i.e. an edge with no siblings.

MATHEMATICA

CoefficientList[Series[(x*(1-Sqrt[1-4*x])/(2*x) + 2*x^3*((1-Sqrt[1-4*x])/(2*x))^4)/(1-x), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 01 2014 *)

PROG

(PARI)

x = 'x + O('x^66);

C = serreverse( x/( 1/(1-x) ) ) / x; \\ Catalan A000108

gf = (x*C+2*x^3*C^4)/(1-x);

concat([0], Vec(gf) ) \\ Joerg Arndt, Aug 21 2013

CROSSREFS

Cf. A000108, A228178.

Sequence in context: A138747 A052975 A275943 * A035929 A071646 A114627

Adjacent sequences:  A228177 A228178 A228179 * A228181 A228182 A228183

KEYWORD

nonn

AUTHOR

Louis Shapiro, Aug 20 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 18:37 EST 2019. Contains 329865 sequences. (Running on oeis4.)