A255638 Number of n-node rooted trees with a forbidden limb of length 8.

1, 1, 2, 4, 9, 20, 48, 115, 285, 717, 1837, 4753, 12451, 32878, 87549, 234654, 632814, 1715446, 4672544, 12780511, 35091842, 96684570, 267223650, 740691451, 2058470490, 5734620428, 16011730686, 44799543203, 125587727914, 352696990890, 992169406959

Offset

1,3

Comments

Any rootward 8-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 = 2.95534758805897943282870965508636011438518881375... and c = 0.43969195292137654501555629074396535899093... . - Vaclav Kotesovec, Feb 28 2016

Maple

with(numtheory):
g:= proc(n, k) option remember; `if`(n=0, 1, add(add(d*(g(d-1, k)-
      `if`(d=k, 1, 0)), d=divisors(j))*g(n-j, k), j=1..n)/n)
    end:
a:= n-> g(n-1, 8):
seq(a(n), n=1..40);

Crossrefs

Column k=8 of A255636.

Sequence in context: A182378 A318801 A318854 * A215971 A034825 A145546

Adjacent sequences: A255635 A255636 A255637 * A255639 A255640 A255641

Keyword

nonn

Author

Alois P. Heinz, Feb 28 2015

Status

approved