A124346 Number of rooted identity trees on n nodes with thinning limbs.

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

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: A318849 A339587 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