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

3,2

Links

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

Formula

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

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);

Crossrefs

Column k=3 of A203717.

Cf. A001006, A036765.

Sequence in context: A171309 A210781 A367818 * A289802 A071719 A370034

Adjacent sequences: A303268 A303269 A303270 * A303272 A303273 A303274

Keyword

nonn

Author

Alois P. Heinz, Apr 20 2018

Status

approved