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

3,4

Links

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

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);

Crossrefs

Column k=3 of A318758.

Sequence in context: A309301 A323798 A180488 * A318818 A026599 A061647

Adjacent sequences: A318857 A318858 A318859 * A318861 A318862 A318863

Keyword

nonn

Author

Alois P. Heinz, Sep 04 2018

Status

approved