A319381 Number of plane trees with n nodes where the sequence of branches directly under any given node is a membership-chain.

1, 1, 1, 2, 2, 4, 6, 9, 11, 20, 28, 40, 58, 82, 110, 159, 217, 305, 420, 570, 767, 1042

Offset: 1

Author

Gus Wiseman, Sep 17 2018

Keywords

• nonn
• more

Examples

			The a(9) = 11 membership-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))
		

Links

• Gus Wiseman, The a(15) = 110 membership-chain trees.

Crossrefs

Cf. A000081, A000108, A001003, A005043, A007562, A118376, A316470, A319122, A319379, A319380, A319436.

Programs

Mathematica

yanplane[n_]:=If[n==1,{{}},Join@@Table[Select[Tuples[yanplane/@c],And@@MemberQ@@@Partition[#,2,1]&],{c,Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[yanplane[n]],{n,10}]