A318861 Number of rooted trees with n nodes such that four equals the maximal number of isomorphic subtrees extending from the same node.

0, 1, 1, 3, 8, 23, 61, 167, 461, 1285, 3587, 10069, 28350, 80101, 226861, 644064, 1832113, 5221138, 14902620, 42597586, 121917123, 349343846, 1002080752, 2877234480, 8268665140, 23782254063, 68454314588, 197176382059, 568320901793, 1639070974728, 4729877188814

Offset

4,4

Links

Alois P. Heinz, Table of n, a(n) for n = 4..2143

Maple

h:= proc(n, m, t, k) option remember; `if`(m=0, binomial(n+t, t),
      `if`(n=0, 0, add(h(n-1, m-j, t+1, k), j=1..min(k, m))))
    end:
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(b(n-i*j, i-1, k)*h(A(i, k), j, 0, k), j=0..n/i)))
    end:
A:= (n, k)-> `if`(n<2, n, b(n-1$2, k)):
a:= n-> (k-> A(n, k)-A(n, k-1))(4):
seq(a(n), n=4..34);

Crossrefs

Column k=4 of A318758.

Sequence in context: A027244 A108457 A071618 * A318819 A146998 A261329

Adjacent sequences: A318858 A318859 A318860 * A318862 A318863 A318864

Keyword

nonn

Author

Alois P. Heinz, Sep 04 2018

Status

approved