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A319379
Number of plane trees with n nodes where the sequence of branches directly under any given node is a chain of multisets.
4
1, 1, 2, 4, 9, 19, 43, 93, 207, 452, 997, 2176, 4776, 10418, 22781, 49674, 108421
OFFSET
1,3
EXAMPLE
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)))
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}]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 17 2018
STATUS
approved