A316474 Number of locally stable rooted identity trees with n nodes, meaning no branch is a subset of any other branch of the same root.

1, 1, 1, 1, 1, 2, 3, 5, 8, 14, 23, 42, 73, 133, 241, 442, 812, 1508, 2802, 5247, 9842, 18554, 35045, 66453, 126249

Offset

1,6

Links

Table of n, a(n) for n=1..25.

Gus Wiseman, The a(10) = 14 locally stable rooted identity trees with 10 nodes.

Example

The a(9) = 8 locally stable rooted identity trees:
((((((((o))))))))
(((((o)((o))))))
((((o)(((o))))))
(((o)((((o))))))
((((o))(((o)))))
((o)(((((o))))))
((o)((o)((o))))
(((o))((((o)))))

Mathematica

strut[n_]:=strut[n]=If[n===1, {{}}, Select[Join@@Function[c, Union[Sort/@Tuples[strut/@c]]]/@IntegerPartitions[n-1], UnsameQ@@#&&Select[Tuples[#, 2], UnsameQ@@#&&Complement@@#=={}&]=={}&]];
Table[Length[strut[n]], {n, 20}]

Crossrefs

Cf. A000081, A004111, A276625, A277098, A285572, A285573, A303362, A304713, A316467, A316471, A316471, A316475.

Sequence in context: A194850 A062692 A182024 * A086661 A018154 A340215

Adjacent sequences: A316471 A316472 A316473 * A316475 A316476 A316477

Keyword

nonn,more

Author

Gus Wiseman, Jul 04 2018

Status

approved