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

Author

Alois P. Heinz, Sep 04 2018

Keywords

• nonn

Links

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

Crossrefs

Column k=4 of A318758.

Programs

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);