A052326 Number of asymmetric trees with a forbidden limb of length 3.

1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 6, 11, 25, 49, 105, 211, 444, 903, 1880, 3865, 8042, 16658, 34764, 72484, 151856, 318418, 669934, 1411637, 2982407, 6311760, 13387127, 28442458, 60543586, 129084965, 275683061, 589660911, 1263128375

Offset: 0

Author

Christian G. Bower, Dec 15 1999

Keywords

• nonn

Comments

A tree with a forbidden limb of length k is a tree where the path from any leaf inward hits a branching node or another leaf within k steps.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
• Index entries for sequences related to Lyndon words

Crossrefs

Cf. A002955, A002988-A002992, A052318-A052329.

Formula

G.f.: 1 + B(x) + x^4 + x^5 + x^6 - (B(x^2) + B(x)^2)/2 where B(x) is g.f. of A052325.

a(n) ~ c * d^n / n^(5/2), where d = 2.2767145838879762709809174486..., c = 0.15900430026983804503695298... . - Vaclav Kotesovec, Aug 25 2014

Extensions

More terms, formula and comments from Christian G. Bower, Dec 15 1999

Typo in cross-reference corrected by Vaclav Kotesovec, Aug 25 2014