A318048 - OEIS

A318048

Size of the span of the unlabeled rooted tree with Matula-Goebel number n.

1, 2, 3, 2, 4, 4, 4, 2, 6, 6, 5, 4, 6, 3, 9, 2, 6, 6, 4, 6, 6, 8, 10, 4, 12, 6, 10, 4, 9, 9, 6, 2, 12, 6, 9, 6, 6, 4, 9, 6, 9, 7, 6, 8, 15, 10, 15, 4, 5, 12, 9, 7, 4, 10, 16, 4, 7, 9, 8, 9, 10, 10, 11, 2, 13, 12, 6, 7, 14, 10, 9, 6, 10, 7, 21, 3, 12, 10, 12, 6

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OFFSET

1,2

COMMENTS

The span of a tree is defined to be the set of possible terminal subtrees of initial subtrees, or, which is the same, the set of possible initial subtrees of terminal subtrees.

LINKS

Table of n, a(n) for n=1..80.

Index entries for sequences related to Matula-Goebel numbers

EXAMPLE

42 is the Matula-Goebel number of (o(o)(oo)), which has span {o, (o), (oo), (ooo), (oo(oo)), (o(o)o), (o(o)(oo))}, so a(42) = 7.

MATHEMATICA

ext[c_, {}]:=c; ext[c_, s:{__}]:=Extract[c, s]; rpp[c_, v_, {}]:=v; rpp[c_, v_, s:{__}]:=ReplacePart[c, v, s];

RLO[ear_, rue:{__}]:=Union@@(Function[x, rpp[ear, x, #2]]/@ReplaceList[ext[ear, #2], #1]&@@@Select[Tuples[{rue, Position[ear, _]}], MatchQ[ext[ear, #[[2]]], #[[1, 1]]]&]);

RL[ear_, rue:{__}]:=FixedPoint[Function[keeps, Union[keeps, Join@@(RLO[#, rue]&/@keeps)]], {ear}];

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

MGTree[n_]:=If[n==1, {}, MGTree/@primeMS[n]];

Table[Length[Union[Cases[RL[MGTree[n], {List[__List]:>List[]}], _List, {1, Infinity}]]], {n, 100}]

CROSSREFS

Cf. A000081, A007097, A007853, A049076, A061773, A061775, A109082, A109129, A206491, A317713, A318046.

Sequence in context: A087437 A304739 A304735 * A235805 A168231 A235728

Adjacent sequences: A318045 A318046 A318047 * A318049 A318050 A318051

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 13 2018

STATUS

approved