A255639 Number of n-node rooted trees with a forbidden limb of length 9.

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

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