A324843 Number of unlabeled rooted trees with n nodes where the branches of any branch of any terminal subtree form a submultiset of the branches of the same subtree.

1, 1, 1, 2, 2, 4, 4, 8, 9, 15, 17, 31, 35, 57, 70, 111, 136, 213, 265, 405, 517, 763, 987, 1458, 1893, 2736, 3611, 5161, 6836, 9702

Offset

1,4

Comments

A subset of totally transitive rooted trees (A318185).

Links

Table of n, a(n) for n=1..30.

Example

The a(1) = 1 through a(8) = 8 rooted trees:
  o  (o)  (oo)  (ooo)   (oooo)   (ooooo)    (oooooo)    (ooooooo)
                (o(o))  (oo(o))  (oo(oo))   (ooo(oo))   (ooo(ooo))
                                 (ooo(o))   (oooo(o))   (oooo(oo))
                                 (o(o)(o))  (oo(o)(o))  (ooooo(o))
                                                        (oo(o)(oo))
                                                        (ooo(o)(o))
                                                        (o(o)(o)(o))
                                                        (o(o)(o(o)))

Mathematica

submultQ[cap_, fat_]:=And@@Function[i, Count[fat, i]>=Count[cap, i]]/@Union[List@@cap];
rallt[n_]:=Select[Union[Sort/@Join@@(Tuples[rallt/@#]&/@IntegerPartitions[n-1])], And@@Table[submultQ[b, #], {b, #}]&];
Table[Length[rallt[n]], {n, 10}]

Crossrefs

The Matula-Goebel numbers of these trees are given by A324842.

Cf. A000081, A279861, A290689, A290822, A318185.

Cf. A324704, A324736, A324748, A324753, A324847, A324848, A324854.

Sequence in context: A351788 A183565 A222708 * A306692 A356236 A120803

Adjacent sequences: A324840 A324841 A324842 * A324844 A324845 A324846

Keyword

nonn,more

Author

Gus Wiseman, Mar 18 2019

Status

approved