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Number of locally stable rooted trees with n nodes, meaning no branch is a submultiset of any other (unequal) branch of the same root.
25

%I #10 Sep 14 2018 02:48:58

%S 1,1,2,3,5,7,14,25,50,101,207,426,902,1917,4108,8887,19335,42330,

%T 93130,205894,456960,1018098,2275613,5102248,11471107,25856413

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

%H Gus Wiseman, <a href="/A316475/a316475.png">The a(8) = 25 locally stable rooted trees with 8 nodes.</a>

%e The a(6) = 7 locally stable rooted trees:

%e (((((o)))))

%e ((((oo))))

%e (((ooo)))

%e (((o)(o)))

%e ((oooo))

%e ((o)((o)))

%e (ooooo)

%t submultisetQ[M_,N_]:=Or[Length[M]==0,MatchQ[{Sort[List@@M],Sort[List@@N]},{{x_,Z___},{___,x_,W___}}/;submultisetQ[{Z},{W}]]]

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

%t Table[Length[strut[n]],{n,15}]

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

%K nonn,more

%O 1,3

%A _Gus Wiseman_, Jul 04 2018

%E a(21)-a(26) from _Robert Price_, Sep 13 2018