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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.
12
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).
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.
Sequence in context: A351788 A183565 A222708 * A306692 A356236 A120803
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Mar 18 2019
STATUS
approved