A255640 Number of n-node rooted trees with a forbidden limb of length 10.

1, 1, 2, 4, 9, 20, 48, 115, 286, 719, 1841, 4764, 12481, 32960, 87776, 235286, 634585, 1720432, 4686643, 12820514, 35205696, 97009449, 268152813, 743354197, 2066114863, 5756601111, 16075024226, 44982031393, 126114491755, 354219140948, 996572117396

Offset

1,3

Comments

Any rootward 10-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 = 2.95571752117840968931298175785458006908910495018670567... and c = 0.43989037737488741580897781267482681067388... . - 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=10, 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=10 of A255636.

Sequence in context: A292554 A318803 A318856 * A216403 A145548 A292555

Adjacent sequences: A255637 A255638 A255639 * A255641 A255642 A255643

Keyword

nonn

Author

Alois P. Heinz, Feb 28 2015

Status

approved