A303271 Number of ordered rooted trees with n non-root nodes such that the maximal outdegree equals three.

1, 4, 15, 53, 182, 616, 2070, 6930, 23166, 77429, 258973, 867230, 2908633, 9772556, 32896088, 110949072, 374934201, 1269505482, 4306750577, 14638006449, 49843505965, 170021694271, 580954640775, 1988357053020, 6816047416230, 23400699072231, 80455436055699

Offset: 3

Author

Alois P. Heinz, Apr 20 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..1802

Crossrefs

Column k=3 of A203717.

Cf. A001006, A036765.

Programs

Maple

b:= proc(u, o, k) option remember; `if`(u+o=0, 1,
      add(b(u-j, o+j-1, k), j=1..min(1, u))+
      add(b(u+j-1, o-j, k), j=1..min(k, o)))
    end:
a:= n-> b(0, n, 3)-b(0, n, 2):
seq(a(n), n=3..35);

Formula

a(n) = A036765(n) - A001006(n).