A292050 Matula-Goebel numbers of semi-binary rooted trees.

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 21, 22, 23, 25, 26, 29, 31, 33, 34, 35, 39, 41, 43, 46, 47, 49, 51, 55, 58, 59, 62, 65, 69, 73, 77, 79, 82, 83, 85, 86, 87, 91, 93, 94, 97, 101, 109, 115, 118, 119, 121, 123, 127, 129, 137, 139, 141, 143, 145

Offset

1,2

Comments

An unlabeled rooted tree is semi-binary if all out-degrees are <= 2. The number of semi-binary trees with n nodes is equal to the number of binary trees with n+1 leaves; see A001190.

Links

Table of n, a(n) for n=1..63.

Mathematica

nn=200;
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
semibinQ[n_]:=Or[n===1, With[{m=primeMS[n]}, And[Length[m]<=2, And@@semibinQ/@m]]];
Select[Range[nn], semibinQ]

Crossrefs

Cf. A000081, A001190, A007097, A036656, A061773, A111299, A214577, A291636.

Sequence in context: A167207 A037143 A236105 * A048627 A152757 A062462

Adjacent sequences: A292047 A292048 A292049 * A292051 A292052 A292053

Keyword

nonn

Author

Gus Wiseman, Sep 08 2017

Status

approved