A244532 Number of ordered unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 3.

1, 0, 0, 3, 7, 8, 21, 55, 121, 265, 611, 1379, 3193, 7436, 17085, 39339, 91846, 214549, 500132, 1169267, 2743302, 6445797, 15167805, 35749961, 84390645, 199523566, 472429633, 1120012481, 2658525869, 6318368820, 15034189965, 35811690663, 85393261630

Offset: 4

Author

Joerg Arndt and Alois P. Heinz, Jun 29 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..1000
• Vaclav Kotesovec, Recurrence (of order 9)

Crossrefs

Column k=3 of A244530.

Cf. A244457.

Programs

Maple

b:= proc(n, t, k) option remember; `if`(n=0,
      `if`(t in [0, k], 1, 0), `if`(t>n, 0, add(b(j-1, k$2)*
       b(n-j, max(0, t-1), k), j=1..n)))
    end:
a:= n-> b(n-1, 3$2) -b(n-1, 4$2):
seq(a(n), n=4..40);

Mathematica

b[n_, t_, k_] := b[n, t, k] = If[n == 0, If[t == 0 || t == k, 1, 0], If[t > n, 0, Sum[b[j - 1, k, k]*b[n - j, Max[0, t - 1], k], {j, 1, n}]]]; T[n_, k_] := b[n - 1, k, k] - If[n == 1 && k == 0, 0, b[n - 1, k + 1, k + 1]]; a[n_] := b[n - 1, 3, 3] - b[n - 1, 4, 4]; Table[a[n], {n, 4, 40}] (* Jean-François Alcover, Feb 06 2015, after Maple *)

Formula

a(n) ~ sqrt(sqrt(2)/4 - sqrt(154+112*sqrt(2))/56) * ((sqrt(13+16*sqrt(2))-1)/2)^n / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Jul 02 2014