A255637 Number of n-node rooted trees with a forbidden limb of length 7.

1, 1, 2, 4, 9, 20, 48, 114, 284, 714, 1829, 4731, 12391, 32711, 87084, 233349, 629137, 1705039, 4642999, 12696374, 34851662, 95997401, 265253845, 735035099, 2042203194, 5687771773, 15876641362, 44409566681, 124460776515, 349437246152, 982732274507

Offset

1,3

Comments

Any rootward 7-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 = 2.954528470057707474794966340476752099204837575... and c = 0.43932847920704393138249966062251759371... . - Vaclav Kotesovec, Feb 28 2016

Maple

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, 7):
seq(a(n), n=1..40);

Crossrefs

Column k=7 of A255636.

Sequence in context: A036722 A318800 A318853 * A215796 A034824 A145545

Adjacent sequences: A255634 A255635 A255636 * A255638 A255639 A255640

Keyword

nonn

Author

Alois P. Heinz, Feb 28 2015

Status

approved