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

0,13

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

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

Crossrefs

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

Sequence in context: A072986 A079047 A160966 * A079118 A211054 A034466

Adjacent sequences: A052323 A052324 A052325 * A052327 A052328 A052329

Keyword

nonn

Author

Christian G. Bower, Dec 15 1999

Extensions

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

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

Status

approved