A318863 Number of rooted trees with n nodes such that six equals the maximal number of isomorphic subtrees extending from the same node.

0, 1, 1, 3, 8, 22, 60, 168, 466, 1306, 3677, 10400, 29503, 83964, 239523, 684855, 1961933, 5630300, 16182535, 46576693, 134225427, 387254945, 1118433179, 3233228736, 9354963666, 27089288339, 78501221909, 227643444368, 660560681614, 1917918979943, 5571738217340

Offset

6,4

Links

Alois P. Heinz, Table of n, a(n) for n = 6..2137

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))(6):
seq(a(n), n=6..36);

Crossrefs

Column k=6 of A318758.

Sequence in context: A318823 A318864 A318822 * A318821 A014397 A048503

Adjacent sequences: A318860 A318861 A318862 * A318864 A318865 A318866

Keyword

nonn

Author

Alois P. Heinz, Sep 04 2018

Status

approved