A244534 Number of ordered unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 5.

1, 0, 0, 0, 0, 5, 11, 12, 13, 14, 50, 136, 289, 477, 703, 1255, 2611, 5489, 10902, 19712, 35455, 66651, 130014, 254737, 488041, 920461, 1741642, 3338360, 6453073, 12425997, 23780944, 45451155, 87224392, 168253246, 324863578, 625728091, 1202953325, 2314485753

Offset

6,6

Links

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

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, 5$2) -b(n-1, 6$2):
seq(a(n), n=6..50);

Mathematica

b[n_, t_, k_] := b[n, t, k] = If[n == 0,
     If[MemberQ[{0, k}, t], 1, 0], If[t > n, 0, Sum[b[j-1, k, k]*
     b[n-j, Max[0, t-1], k], {j, n}]]];
a[n_] := b[n-1, 5, 5] - b[n-1, 6, 6];
Table[a[n], {n, 6, 50}] (* Jean-François Alcover, Aug 28 2021, after Maple code *)

Crossrefs

Column k=5 of A244530.

Cf. A244459.

Sequence in context: A289580 A126243 A095805 * A034596 A166275 A122955

Adjacent sequences: A244531 A244532 A244533 * A244535 A244536 A244537

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 29 2014

Status

approved