A318860 Number of rooted trees with n nodes such that three equals the maximal number of isomorphic subtrees extending from the same node.

0, 1, 1, 3, 9, 23, 60, 164, 443, 1209, 3319, 9150, 25326, 70335, 195870, 546823, 1529935, 4288662, 12042447, 33866604, 95373852, 268925258, 759157224, 2145298117, 6068251826, 17180172176, 48680092670, 138041661905, 391725281701, 1112360700816, 3160707529077

Offset: 3

Author

Alois P. Heinz, Sep 04 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..2158

Crossrefs

Column k=3 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))(3):
seq(a(n), n=3..33);