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

4,4

Links

Alois P. Heinz, Table of n, a(n) for n = 4..1000

Vaclav Kotesovec, Recurrence (of order 9)

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

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 *)

Crossrefs

Column k=3 of A244530.

Cf. A244457.

Sequence in context: A125570 A268111 A369920 * A037208 A102007 A152486

Adjacent sequences: A244529 A244530 A244531 * A244533 A244534 A244535

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 29 2014

Status

approved