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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 (list; graph; refs; listen; history; text; internal format)
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 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

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Last modified December 15 22:02 EST 2019. Contains 330012 sequences. (Running on oeis4.)