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A358507 Sorted list of positions of first appearances in the sequence counting permutations of Matula-Goebel trees (A206487). 4
1, 6, 12, 24, 30, 48, 60, 72, 104, 120, 144, 148, 156, 180, 192, 222, 288, 312, 360, 390, 432, 444, 480, 576, 712, 720, 780, 832, 864, 900, 1080, 1110, 1248, 1260, 1296, 1440, 1560, 1680, 2136, 2160, 2262, 2304, 2340, 2496, 2520, 2592, 2738, 2880, 2886, 3072 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
To get a permutation of a tree, we choose a permutation of the multiset of branches of each node.
The Matula-Goebel number of a rooted tree is the product of primes indexed by the Matula-Goebel numbers of the branches of its root, which gives a bijective correspondence between positive integers and unlabeled rooted trees.
LINKS
EXAMPLE
The terms together with their corresponding trees begin:
1: o
6: (o(o))
12: (oo(o))
24: (ooo(o))
30: (o(o)((o)))
48: (oooo(o))
60: (oo(o)((o)))
72: (ooo(o)(o))
104: (ooo(o(o)))
120: (ooo(o)((o)))
144: (oooo(o)(o))
148: (oo(oo(o)))
156: (oo(o)(o(o)))
180: (oo(o)(o)((o)))
192: (oooooo(o))
222: (o(o)(oo(o)))
288: (ooooo(o)(o))
312: (ooo(o)(o(o)))
MATHEMATICA
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]
MGTree[n_Integer]:=If[n===1, {}, MGTree/@primeMS[n]]
treeperms[t_]:=Times@@Cases[t, b:{__}:>Length[Permutations[b]], {0, Infinity}];
fir[q_]:=Select[Range[Length[q]], !MemberQ[Take[q, #-1], q[[#]]]&];
fir[Table[treeperms[MGTree[n]], {n, 100}]]
CROSSREFS
Positions of first appearances in A206487.
The unsorted version is A358508.
A000081 counts rooted trees, ordered A000108.
A214577 and A358377 rank trees with no permutations.
Sequence in context: A261476 A119840 A298033 * A358526 A069171 A071611
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 20 2022
STATUS
approved

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Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)