A324838 Number of unlabeled rooted trees with n nodes where the branches of no branch of the root form a submultiset of the branches of the root.

1, 0, 1, 2, 5, 10, 28, 64, 169, 422, 1108, 2872, 7627, 20202, 54216, 145867, 395288

Offset

1,4

Links

Table of n, a(n) for n=1..17.

Example

The a(1) = 1 through a(6) = 10 rooted trees:
  o  ((o))  ((oo))   ((ooo))    ((oooo))
            (((o)))  (((oo)))   (((ooo)))
                     ((o)(o))   ((o)(oo))
                     ((o(o)))   ((o(oo)))
                     ((((o))))  ((oo(o)))
                                ((((oo))))
                                (((o)(o)))
                                (((o(o))))
                                ((o((o))))
                                (((((o)))))

Mathematica

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

Crossrefs

Cf. A000081, A290689, A304360, A306844, A317787, A318185.

Cf. A324694, A324696, A324704, A324738, A324744, A324758, A324759, A324765, A324768, A324771, A324839, A324840, A324844, A324846.

Sequence in context: A243797 A120896 A074801 * A370316 A257889 A363388

Adjacent sequences: A324835 A324836 A324837 * A324839 A324840 A324841

Keyword

nonn,more

Author

Gus Wiseman, Mar 18 2019

Status

approved