A003228 - OEIS

A003228

Endpoints in trees with n nodes.
(Formerly M0351)

1, 2, 2, 5, 9, 21, 43, 101, 226, 556, 1333, 3365, 8500, 22007, 57258, 151264, 401761, 1077063, 2902599, 7871250, 21440642, 58672589, 161155637, 444240627, 1228400744, 3406668865, 9472308269, 26402207803, 73755064178

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..29.

R. W. Robinson and A. J. Schwenk, The distribution of trees in a large random tree, Discr. Math., 12 (1975), 359-372.

Eric Weisstein's World of Mathematics, Tree Leaf.

Index entries for sequences related to trees

FORMULA

a(n) = Sum_{k=1..n} k*c(n, k), where c(n, k) = A055290(n, k) has g.f. (1-x+x*y)*B(x, y)+(1/2)*(B(x^2, y^2)-B(x, y)^2) and B(x, y) is g.f. for A055372.

CROSSREFS

Cf. A000055, A003227, A055290, A055372.

Sequence in context: A002990 A060405 A326493 * A184713 A110182 A309867

Adjacent sequences: A003225 A003226 A003227 * A003229 A003230 A003231

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Corrected and extended with formula by Christian G. Bower, May 25 2000

STATUS

approved