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A255639 Number of n-node rooted trees with a forbidden limb of length 9. 2
1, 1, 2, 4, 9, 20, 48, 115, 286, 718, 1840, 4761, 12473, 32938, 87716, 235119, 634120, 1719126, 4682962, 12810093, 35176103, 96925151, 267912108, 742665338, 2064139687, 5750927832, 16058703976, 44935017987, 125978892299, 353827590946, 995440328858 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Any rootward 9-node path starting at a leaf contains the root or a branching node.

LINKS

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

FORMULA

a(n) ~ c * d^n / n^(3/2), where d = 2.95562406748808419554567595195333686205085952464972655... and c = 0.439835068532467809288350528155403598039874... . - Vaclav Kotesovec, Feb 28 2016

MAPLE

with(numtheory):

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

      `if`(d=9, 1, 0)), d=divisors(j))*g(n-j), j=1..n)/n)

    end:

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

seq(a(n), n=1..40);

CROSSREFS

Column k=9 of A255636.

Sequence in context: A292553 A318802 A318855 * A216062 A034826 A145547

Adjacent sequences:  A255636 A255637 A255638 * A255640 A255641 A255642

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 28 2015

STATUS

approved

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Last modified October 17 19:18 EDT 2019. Contains 328127 sequences. (Running on oeis4.)