login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A052327 Number of rooted trees with a forbidden limb of length 4. 2
1, 1, 2, 4, 8, 18, 43, 102, 251, 625, 1584, 4055, 10509, 27451, 72307, 191697, 511335, 1370995, 3693452, 9991671, 27133149, 73934800, 202096673, 553999573, 1522651908, 4195087022, 11583820212, 32052475655, 88860186023 (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(4)=1, b(k)=0 if k != 4.

a(n) ~ c * d^n / n^(3/2), where d = 2.9224691962496551739365155005926289..., c = 0.43112017460637374030857983498164... . - 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=4, 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.

Sequence in context: A027056 A024428 A049075 * A059221 A193617 A233139

Adjacent sequences:  A052324 A052325 A052326 * A052328 A052329 A052330

KEYWORD

nonn

AUTHOR

Christian G. Bower, Dec 15 1999.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 28 21:04 EST 2014. Contains 250406 sequences.