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A124346 Number of rooted identity trees on n nodes with thinning limbs. 5
1, 1, 1, 2, 2, 4, 6, 11, 17, 32, 56, 102, 184, 340, 624, 1161, 2156, 4036, 7562, 14234, 26828, 50747, 96125, 182545, 347187, 661618, 1262583, 2413275, 4618571, 8850905, 16981142, 32616900, 62713951, 120703497, 232527392, 448344798, 865182999, 1670884073 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A rooted tree with thinning limbs is such that if a node has k children, all its children have at most k children.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..140

EXAMPLE

The a(7) = 6 trees are ((((((o)))))), (o((((o))))), (o(o((o)))), ((o)(((o)))), ((o)(o(o))), (o(o)((o))). - Gus Wiseman, Jan 25 2018

MATHEMATICA

idthinQ[t_]:=And@@Cases[t, b_List:>UnsameQ@@b&&Length[b]>=Max@@Length/@b, {0, Infinity}];

itrut[n_]:=itrut[n]=If[n===1, {{}}, Select[Join@@Function[c, Union[Sort/@Tuples[itrut/@c]]]/@IntegerPartitions[n-1], idthinQ]];

Table[Length[itrut[n]], {n, 25}] (* Gus Wiseman, Jan 25 2018 *)

CROSSREFS

Cf. A000081, A001678, A003238, A004111, A124343-A124348, A276625, A290689, A298303-A298305, A298422.

Row sums of A245120.

Sequence in context: A216958 A318849 A293014 * A300797 A033961 A298163

Adjacent sequences:  A124343 A124344 A124345 * A124347 A124348 A124349

KEYWORD

nonn

AUTHOR

Christian G. Bower, Oct 30 2006, suggested by Franklin T. Adams-Watters

STATUS

approved

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Last modified March 24 01:20 EDT 2019. Contains 321444 sequences. (Running on oeis4.)