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A052328 Number of rooted trees with a forbidden limb of length 5. 4
1, 1, 2, 4, 9, 19, 46, 110, 273, 684, 1747, 4505, 11763, 30956, 82153, 219437, 589747, 1593170, 4324445, 11787195, 32251520, 88548011, 243877256, 673605521, 1865445693, 5178574184, 14408195935, 40170674295, 112213616851 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

N. J. A. Sloane, Transforms

Index entries for sequences related to rooted trees

FORMULA

a(n) satisfies a = SHIFT_RIGHT(EULER(a-b)) where b(5)=1, b(k)=0 if k != 5.

a(n) ~ c * d^n / n^(3/2), where d = 2.944791657501974377513779510930324..., c = 0.43624554592719796037836168844839... . - Vaclav Kotesovec, Aug 25 2014

MAPLE

with(numtheory):

g:= proc(n) g(n):= `if`(n=0, 1, add(add(d*(g(d-1)-

      `if`(d=5, 1, 0)), d=divisors(j))*g(n-j), j=1..n)/n)

    end:

a:= n-> g(n-1):

seq(a(n), n=1..35);  # Alois P. Heinz, Jul 04 2014

CROSSREFS

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

Column k=5 of A255636.

Sequence in context: A134964 A318798 A318851 * A133228 A036717 A000080

Adjacent sequences:  A052325 A052326 A052327 * A052329 A052330 A052331

KEYWORD

nonn

AUTHOR

Christian G. Bower, Dec 15 1999

STATUS

approved

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Last modified October 22 23:18 EDT 2018. Contains 316518 sequences. (Running on oeis4.)