A244533 Number of ordered unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 4.

1, 0, 0, 0, 4, 9, 10, 11, 34, 91, 196, 330, 636, 1377, 2976, 6061, 12199, 25186, 52767, 109066, 224964, 467605, 979056, 2042847, 4244986, 8844130, 18527956, 38878929, 81460220, 170576593, 357894472, 752544917, 1583579674, 3332453026, 7016669752, 14790212086

Offset

5,5

Links

Alois P. Heinz, Table of n, a(n) for n = 5..1000

Vaclav Kotesovec, Recurrence (of order 11)

Formula

a(n) ~ c * d^n / (sqrt(Pi) * n^(3/2)), where d = 2.18452974131524781307797151868229485574758... is the root of the equation -229 - 36*d + 2*d^2 - 32*d^3 + 19*d^4 + 4*d^5 = 0, and c = 0.181069926661856899940163775713243367029404419526724... . - 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, 4$2) -b(n-1, 5$2):
seq(a(n), n=5..45);

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, 4, 4] - b[n - 1, 5, 5]; Table[a[n], {n, 5, 45}] (* Jean-François Alcover, Feb 06 2015, after Maple *)

Crossrefs

Column k=4 of A244530.

Cf. A244458.

Sequence in context: A125726 A352323 A175308 * A180149 A155879 A172192

Adjacent sequences: A244530 A244531 A244532 * A244534 A244535 A244536

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 29 2014

Status

approved