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A317785 Number of locally connected rooted trees with n nodes. 4
1, 1, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, 34, 42, 55, 67, 91, 109, 144, 177, 228, 281, 366, 448, 579, 720, 916, 1142 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

An unlabeled rooted tree is locally connected if the branches directly under any given node are connected as a hypergraph.

LINKS

Table of n, a(n) for n=1..30.

Gus Wiseman, All 42 locally connected rooted trees with 16 nodes.

EXAMPLE

The a(11) = 12 locally connected rooted trees:

  ((((((((((o))))))))))

  ((((((((o)(o))))))))

  (((((((o))((o)))))))

  ((((((o)))(((o))))))

  (((((o))))((((o)))))

  ((((((o)(o)(o))))))

  (((((o))((o)(o)))))

  ((((o))((o))((o))))

  ((((o)(o)(o)(o))))

  (((o))((o)(o)(o)))

  (((o)(o))((o)(o)))

  ((o)(o)(o)(o)(o))

MATHEMATICA

multijoin[mss__]:=Join@@Table[Table[x, {Max[Count[#, x]&/@{mss}]}], {x, Union[mss]}];

csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Union[Append[Delete[s, List/@c[[1]]], multijoin@@s[[c[[1]]]]]]]]];

rurt[n_]:=If[n==1, {{}}, Join@@Table[Select[Union[Sort/@Tuples[rurt/@ptn]], Or[Length[#]==1, Length[csm[#]]==1]&], {ptn, IntegerPartitions[n-1]}]];

Table[Length[rurt[n]], {n, 10}]

CROSSREFS

Cf. A000081, A276625, A286518, A286520, A301700, A304714, A316473, A316475, A317077, A317078, A317708, A317787.

Sequence in context: A002865 A085811 A187219 * A014810 A318771 A239835

Adjacent sequences:  A317782 A317783 A317784 * A317786 A317787 A317788

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 06 2018

STATUS

approved

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Last modified November 13 12:45 EST 2019. Contains 329094 sequences. (Running on oeis4.)