A318859 Number of rooted trees with n nodes such that two equals the maximal number of isomorphic subtrees extending from the same node.

0, 1, 1, 4, 9, 22, 54, 138, 346, 889, 2285, 5928, 15436, 40424, 106230, 280305, 741912, 1969816, 5243942, 13995807, 37439883, 100371907, 269623436, 725638613, 1956352468, 5283171593, 14289645110, 38707131195, 104995130162, 285184002486, 775586517781

Offset

2,4

Links

Alois P. Heinz, Table of n, a(n) for n = 2..2213

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))(2):
seq(a(n), n=2..32);

Mathematica

h[n_, m_, t_, k_] := h[n, m, t, k] = If[m == 0, Binomial[n + t, t],
   If[n == 0, 0, Sum[h[n - 1, m - j, t + 1, k], {j, 1, Min[k, m]}]]];
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0,
   Sum[b[n - i*j, i - 1, k]*h[A[i, k], j, 0, k], {j, 0, n/i}]]];
A[n_, k_] := If[n < 2, n, b[n - 1, n - 1, k]];
a[n_] := A[n, 2] - A[n, 1];
Table[a[n], {n, 2, 32}] (* Jean-François Alcover, Dec 01 2023, after Alois P. Heinz *)

Crossrefs

Column k=2 of A318758.

Sequence in context: A076859 A042833 A048654 * A318817 A122626 A135025

Adjacent sequences: A318856 A318857 A318858 * A318860 A318861 A318862

Keyword

nonn

Author

Alois P. Heinz, Sep 04 2018

Status

approved