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

Author

Alois P. Heinz, Feb 28 2015

Keywords

• nonn

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

Crossrefs

Column k=10 of A255636.

Programs

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);

Formula

a(n) ~ c * d^n / n^(3/2), where d = 2.95571752117840968931298175785458006908910495018670567... and c = 0.43989037737488741580897781267482681067388... . - Vaclav Kotesovec, Feb 28 2016