A318899 Number of n-node rooted trees in which three 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, 7, 18, 45, 116, 298, 776, 2025, 5322, 14030, 37155, 98685, 262961, 702497, 1881475, 5050140, 13583622, 36605565, 98821445, 267220361, 723704046, 1962830775, 5330900916, 14497096134, 39472561082, 107601053713, 293643574776, 802203904616, 2193758306687

Offset

3,3

Links

Alois P. Heinz, Table of n, a(n) for n = 3..2209

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))(3):
seq(a(n), n=3..35);

Crossrefs

Column k=3 of A255704.

Sequence in context: A247296 A191652 A191826 * A114713 A078058 A116413

Adjacent sequences: A318896 A318897 A318898 * A318900 A318901 A318902

Keyword

nonn

Author

Alois P. Heinz, Sep 05 2018

Status

approved