A244458 Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 4.

1, 0, 0, 0, 1, 2, 2, 2, 4, 7, 12, 16, 25, 38, 61, 94, 147, 227, 356, 550, 862, 1345, 2113, 3299, 5168, 8091, 12721, 19981, 31421, 49384, 77761, 122487, 193151, 304623, 480852, 759367, 1200150, 1897594, 3002329, 4752436, 7527155, 11927290, 18909719, 29993579

Offset

5,6

Links

Alois P. Heinz, Table of n, a(n) for n = 5..900

Example

a(9) = 1:
         o
      / ( ) \
     o  o o  o
   /( )\
  o o o o

Maple

b:= proc(n, i, t, k) option remember; `if`(n=0, `if`(t in [0, k],
      1, 0), `if`(i<1 or t>n, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
      b(n-i*j, i-1, max(0, t-j), k), j=0..n/i)))
    end:
a:= n-> b(n-1$2, 4$2) -b(n-1$2, 5$2):
seq(a(n), n=5..50);

Mathematica

b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, If[t == 0 || t == k, 1, 0], If[i < 1, 0, Sum[Binomial[b[i - 1, i - 1, k, k] + j - 1, j]*b[n - i*j, i - 1, Max[0, t - j], k], {j, 0, n/i}]] // FullSimplify]; a[n_] := b[n - 1, n - 1, 4, 4] - b[n - 1, n - 1, 5, 5]; Table[a[n], {n, 5, 50}] (* Jean-François Alcover, Feb 06 2015, after Maple *)

Crossrefs

Column k=4 of A244454.

Cf. A244533.

Sequence in context: A253059 A098705 A029866 * A286613 A229061 A339464

Adjacent sequences: A244455 A244456 A244457 * A244459 A244460 A244461

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 29 2014

Status

approved