A319380 Number of plane trees with n nodes where the sequence of branches directly under any given node is a chain of distinct multisets.

1, 1, 1, 2, 3, 5, 9, 17, 30, 53, 94, 169, 303, 543, 968, 1728, 3080, 5491, 9776, 17415, 31008

Offset: 1

Author

Gus Wiseman, Sep 17 2018

Keywords

• nonn
• more

Examples

			The a(8) = 17 locally identity chain trees:
  (((((((o)))))))  (((((o(o))))))  (((o(o(o)))))  (o(o(o(o))))
                   ((((o((o))))))  ((o((o(o)))))  (o(o)(o(o)))
                   (((o(((o))))))  ((o(o((o)))))
                   ((o((((o))))))  (((o)(o(o))))
                   (o(((((o))))))  (o(((o(o)))))
                                   (o((o((o)))))
                                   (o(o(((o)))))
                                   ((o)(o((o))))
                                   (((o))(o(o)))
		

Links

• Gus Wiseman, The a(12) = 169 identity chain trees.

Crossrefs

Cf. A000081, A000108, A001003, A005043, A007562, A118376, A316470, A319122, A319379, A319381.

Programs

Mathematica

submultisetQ[M_,N_]:=Or[Length[M]==0,MatchQ[{Sort[List@@M],Sort[List@@N]},{{x_,Z___},{_,x_,W___}}/;submultisetQ[{Z},{W}]]];
idchnplane[n_]:=If[n==1,{{}},Join@@Table[Select[Tuples[idchnplane/@c],And[UnsameQ@@#,And@@submultisetQ@@@Partition[#,2,1]]&],{c,Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[idchnplane[n]],{n,10}]