A318900 Number of n-node rooted trees in which four equals the maximal number of nodes in paths starting at a leaf and ending at the first branching node or at the root.

1, 1, 3, 8, 21, 56, 152, 413, 1131, 3113, 8603, 23861, 66386, 185190, 517807, 1450836, 4072474, 11450141, 32240466, 90901507, 256605905, 725176409, 2051455548, 5808817638, 16462274560, 46691893949, 132531324274, 376443234567, 1069953746735, 3042969864371

Offset

4,3

Links

Alois P. Heinz, Table of n, a(n) for n = 4..2158

Maple

g:= proc(n, k) option remember; `if`(n=0, 1, add(add(d*(g(d-1, k)-
      `if`(d=k, 1, 0)), d=numtheory[divisors](j))*g(n-j, k), j=1..n)/n)
    end:
a:= n-> (k-> g(n-1, k) -g(n-1, k-1))(4):
seq(a(n), n=4..35);

Crossrefs

Column k=4 of A255704.

Sequence in context: A090413 A128105 A085560 * A243633 A094374 A008909

Adjacent sequences: A318897 A318898 A318899 * A318901 A318902 A318903

Keyword

nonn

Author

Alois P. Heinz, Sep 05 2018

Status

approved