cp's OEIS Frontend

A324844 Number of unlabeled rooted trees with n nodes where the branches of no non-leaf branch of any terminal subtree form a submultiset of the branches of the same subtree.

%I A324844 #5 Mar 19 2019 07:15:13
%S A324844 1,1,2,3,7,13,32,71,170,406,1002,2469,6204,15644,39871,102116,263325,
%T A324844 682079,1775600,4640220
%N A324844 Number of unlabeled rooted trees with n nodes where the branches of no non-leaf branch of any terminal subtree form a submultiset of the branches of the same subtree.
%e A324844 The a(1) = 1 through a(6) = 13 rooted trees:
%e A324844   o  (o)  (oo)   (ooo)    (oooo)     (ooooo)
%e A324844           ((o))  ((oo))   ((ooo))    ((oooo))
%e A324844                  (((o)))  (o(oo))    (o(ooo))
%e A324844                           (((oo)))   (((ooo)))
%e A324844                           ((o)(o))   ((o)(oo))
%e A324844                           (o((o)))   ((o(oo)))
%e A324844                           ((((o))))  (o((oo)))
%e A324844                                      (oo((o)))
%e A324844                                      ((((oo))))
%e A324844                                      (((o)(o)))
%e A324844                                      ((o((o))))
%e A324844                                      (o(((o))))
%e A324844                                      (((((o)))))
%t A324844 submultQ[cap_,fat_]:=And@@Function[i,Count[fat,i]>=Count[cap,i]]/@Union[List@@cap];
%t A324844 rallt[n_]:=Select[Union[Sort/@Join@@(Tuples[rallt/@#]&/@IntegerPartitions[n-1])],And@@Table[!submultQ[b,#],{b,DeleteCases[#,{}]}]&];
%t A324844 Table[Length[rallt[n]],{n,10}]
%Y A324844 The Matula-Goebel numbers of these trees are given by A324845.
%Y A324844 Cf. A000081, A290689, A306844, A318185.
%Y A324844 Cf. A324694, A324738, A324744, A324749, A324754, A324759, A324765, A324768, A324838, A324843, A324846, A324847, A324848, A324849.
%K A324844 nonn
%O A324844 1,3
%A A324844 _Gus Wiseman_, Mar 18 2019