A319379 - OEIS

%I #7 Sep 19 2018 09:18:00

%S 1,1,2,4,9,19,43,93,207,452,997,2176,4776,10418,22781,49674,108421

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

%H Gus Wiseman, <a href="/A319379/a319379.png">The a(9) = 207 chain trees.</a>

%e The a(6) = 19 chain trees:

%e   (((((o)))))  ((((oo))))  (((ooo)))  ((oooo))  (ooooo)

%e                (((o)(o)))  ((o)(oo))  (o(ooo))

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

%e                ((o((o))))  ((oo(o)))  (ooo(o))

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

%e                            (o(o)(o))

%e                            (o(o(o)))

%e                            (oo((o)))

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

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

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

%Y Cf. A000081, A000108, A001003, A005043, A007562, A118376, A143363, A316470, A319122, A319378, A319380, A319381.

%K nonn,more

%O 1,3

%A _Gus Wiseman_, Sep 17 2018