A324845 -id:A324845 - 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.

1, 1, 2, 3, 7, 13, 32, 71, 170, 406, 1002, 2469, 6204, 15644, 39871, 102116, 263325, 682079, 1775600, 4640220

Offset: 1

Gus Wiseman, Mar 18 2019

nonn

			The a(1) = 1 through a(6) = 13 rooted trees:
  o  (o)  (oo)   (ooo)    (oooo)     (ooooo)
          ((o))  ((oo))   ((ooo))    ((oooo))
                 (((o)))  (o(oo))    (o(ooo))
                          (((oo)))   (((ooo)))
                          ((o)(o))   ((o)(oo))
                          (o((o)))   ((o(oo)))
                          ((((o))))  (o((oo)))
                                     (oo((o)))
                                     ((((oo))))
                                     (((o)(o)))
                                     ((o((o))))
                                     (o(((o))))
                                     (((((o)))))

The Matula-Goebel numbers of these trees are given by A324845.
Cf. A000081, A290689, A306844, A318185.
Cf. A324694, A324738, A324744, A324749, A324754, A324759, A324765, A324768, A324838, A324843, A324846, A324847, A324848, A324849.

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,DeleteCases[#,{}]}]&];
Table[Length[rallt[n]],{n,10}]

A324769 Matula-Goebel numbers of fully anti-transitive rooted trees.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 35, 37, 41, 43, 47, 49, 51, 53, 57, 59, 61, 63, 64, 65, 67, 71, 73, 77, 79, 81, 83, 85, 89, 91, 95, 97, 101, 103, 107, 109, 113, 115, 121, 125, 127, 128, 129, 131, 133, 137, 139, 143, 147

Offset: 1

Gus Wiseman, Mar 17 2019

nonn

An unlabeled rooted tree is fully anti-transitive if no proper terminal subtree of any branch of the root is a branch of the root.

			The sequence of fully anti-transitive rooted trees together with their Matula-Goebel numbers begins:
   1: o
   2: (o)
   3: ((o))
   4: (oo)
   5: (((o)))
   7: ((oo))
   8: (ooo)
   9: ((o)(o))
  11: ((((o))))
  13: ((o(o)))
  16: (oooo)
  17: (((oo)))
  19: ((ooo))
  21: ((o)(oo))
  23: (((o)(o)))
  25: (((o))((o)))
  27: ((o)(o)(o))
  29: ((o((o))))
  31: (((((o)))))
  32: (ooooo)
  35: (((o))(oo))
  37: ((oo(o)))
  41: (((o(o))))
  43: ((o(oo)))
  47: (((o)((o))))
  49: ((oo)(oo))

Cf. A000081, A007097, A276625, A290760, A304360, A306844.
Cf. A324695, A324751, A324756, A324758, A324766, A324768, A324770.
Cf. A324838, A324841, A324845, A324846.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
fullantiQ[n_]:=Intersection[Union@@Rest[FixedPointList[Union@@primeMS/@#&,primeMS[n]]],primeMS[n]]=={};
Select[Range[100],fullantiQ]

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.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica