A319381 - OEIS

%I #7 Sep 19 2018 09:18:12

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

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

%H Gus Wiseman, <a href="/A319381/a319381.png">The a(15) = 110 membership-chain trees.</a>

%e The a(9) = 11 membership-chain trees:

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

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

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

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

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

%t Table[Length[yanplane[n]],{n,10}]

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

%K nonn,more

%O 1,4

%A _Gus Wiseman_, Sep 17 2018