A003228 Endpoints in trees with n nodes.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

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

Links

• 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

Crossrefs

Cf. A000055, A003227, A055290, A055372.

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.

Extensions

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