A316475 Number of locally stable rooted trees with n nodes, meaning no branch is a submultiset of any other (unequal) branch of the same root.

1, 1, 2, 3, 5, 7, 14, 25, 50, 101, 207, 426, 902, 1917, 4108, 8887, 19335, 42330, 93130, 205894, 456960, 1018098, 2275613, 5102248, 11471107, 25856413

Offset

1,3

Links

Table of n, a(n) for n=1..26.

Gus Wiseman, The a(8) = 25 locally stable rooted trees with 8 nodes.

Example

The a(6) = 7 locally stable rooted trees:
(((((o)))))
((((oo))))
(((ooo)))
(((o)(o)))
((oooo))
((o)((o)))
(ooooo)

Mathematica

submultisetQ[M_, N_]:=Or[Length[M]==0, MatchQ[{Sort[List@@M], Sort[List@@N]}, {{x_, Z___}, {___, x_, W___}}/; submultisetQ[{Z}, {W}]]]
strut[n_]:=strut[n]=If[n===1, {{}}, Select[Join@@Function[c, Union[Sort/@Tuples[strut/@c]]]/@IntegerPartitions[n-1], Select[Tuples[#, 2], UnsameQ@@#&&submultisetQ@@#&]=={}&]];
Table[Length[strut[n]], {n, 15}]

Crossrefs

Cf. A000081, A285572, A285573, A303362, A304713, A316468, A316470, A316473, A316474.

Sequence in context: A005629 A028304 A324840 * A303875 A331037 A228652

Adjacent sequences: A316472 A316473 A316474 * A316476 A316477 A316478

Keyword

nonn,more

Author

Gus Wiseman, Jul 04 2018

Extensions

a(21)-a(26) from Robert Price, Sep 13 2018

Status

approved