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

1,4

Links

Table of n, a(n) for n=1..22.

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

Example

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))

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}]

Crossrefs

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

Sequence in context: A222735 A299408 A338937 * A340496 A035564 A240065

Adjacent sequences: A319378 A319379 A319380 * A319382 A319383 A319384

Keyword

nonn,more

Author

Gus Wiseman, Sep 17 2018

Status

approved