

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.


24



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
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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[n1], 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 A228652 A157833
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



