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

Author

Gus Wiseman, Jul 04 2018

Keywords

• nonn
• more

Examples

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

Links

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

Crossrefs

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

Programs

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}]

Extensions

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