A319380 - OEIS

%I #6 Sep 19 2018 09:18:06

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

%T 31008

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

%H Gus Wiseman, <a href="/A319380/a319380.png">The a(12) = 169 identity chain trees.</a>

%e The a(8) = 17 locally identity 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)))))

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

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

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

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

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

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

%t submultisetQ[M_,N_]:=Or[Length[M]==0,MatchQ[{Sort[List@@M],Sort[List@@N]},{{x_,Z___},{___,x_,W___}}/;submultisetQ[{Z},{W}]]];

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

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

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

%K nonn,more

%O 1,4

%A _Gus Wiseman_, Sep 17 2018