A244401 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 5.

1, 2, 6, 17, 50, 142, 409, 1169, 3356, 9617, 27601, 79210, 227527, 653793, 1879867, 5407806, 15564968, 44820889, 129127761, 372177974, 1073169150, 3095721985, 8933568154, 25789862435, 74477871565, 215155604291, 621754458752, 1797297119000, 5196966140656

Offset

6,2

Links

Alois P. Heinz, Table of n, a(n) for n = 6..1000

Formula

a(n) = A036721(n) - A036718(n).

Maple

b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
      `if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
       b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
    end:
a:= n-> b(n-1$2, 5$2) -`if`(k=0, 0, b(n-1$2, 4$2)):
seq(a(n), n=6..40);

Mathematica

b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[b[i - 1, i - 1, k, k] + j - 1, j]* b[n - i*j, i - 1, t - j, k], {j, 0, Min[t, n/i]}]] // FullSimplify] ; a[n_] := b[n-1, n-1, 5, 5] - If[n == 0, 0, b[n-1, n-1, 4, 4]]; Table[a[n], {n, 6, 40}] (* Jean-François Alcover, Feb 09 2015, after Maple *)

Crossrefs

Column k=5 of A244372.

Cf. A036718, A036721.

Sequence in context: A336742 A148445 A148446 * A244402 A244403 A244404

Adjacent sequences: A244398 A244399 A244400 * A244402 A244403 A244404

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 27 2014

Status

approved