A324843 - OEIS

%I #6 Mar 19 2019 07:15:01

%S 1,1,1,2,2,4,4,8,9,15,17,31,35,57,70,111,136,213,265,405,517,763,987,

%T 1458,1893,2736,3611,5161,6836,9702

%N 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.

%C A subset of totally transitive rooted trees (A318185).

%e The a(1) = 1 through a(8) = 8 rooted trees:

%e   o  (o)  (oo)  (ooo)   (oooo)   (ooooo)    (oooooo)    (ooooooo)

%e                 (o(o))  (oo(o))  (oo(oo))   (ooo(oo))   (ooo(ooo))

%e                                  (ooo(o))   (oooo(o))   (oooo(oo))

%e                                  (o(o)(o))  (oo(o)(o))  (ooooo(o))

%e                                                         (oo(o)(oo))

%e                                                         (ooo(o)(o))

%e                                                         (o(o)(o)(o))

%e                                                         (o(o)(o(o)))

%t submultQ[cap_,fat_]:=And@@Function[i,Count[fat,i]>=Count[cap,i]]/@Union[List@@cap];

%t rallt[n_]:=Select[Union[Sort/@Join@@(Tuples[rallt/@#]&/@IntegerPartitions[n-1])],And@@Table[submultQ[b,#],{b,#}]&];

%t Table[Length[rallt[n]],{n,10}]

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

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

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

%K nonn,more

%O 1,4

%A _Gus Wiseman_, Mar 18 2019