A319379 Number of plane trees with n nodes where the sequence of branches directly under any given node is a chain of multisets.

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

Offset: 1

Author

Gus Wiseman, Sep 17 2018

Keywords

• nonn
• more

Examples

			The a(6) = 19 chain trees:
  (((((o)))))  ((((oo))))  (((ooo)))  ((oooo))  (ooooo)
               (((o)(o)))  ((o)(oo))  (o(ooo))
               (((o(o))))  ((o(oo)))  (oo(oo))
               ((o((o))))  ((oo(o)))  (ooo(o))
               (o(((o))))  (o((oo)))
                           (o(o)(o))
                           (o(o(o)))
                           (oo((o)))
		

Links

• Gus Wiseman, The a(9) = 207 chain trees.

Crossrefs

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

Programs

Mathematica

submultisetQ[M_,N_]:=Or[Length[M]==0,MatchQ[{Sort[List@@M],Sort[List@@N]},{{x_,Z___},{_,x_,W___}}/;submultisetQ[{Z},{W}]]];
chnplane[n_]:=If[n==1,{{}},Join@@Table[Select[Tuples[chnplane/@c],And@@submultisetQ@@@Partition[#,2,1]&],{c,Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[chnplane[n]],{n,10}]