A319379
Number of plane trees with n nodes where the sequence of branches directly under any given node is a chain of multisets.
Original entry on oeis.org
1, 1, 2, 4, 9, 19, 43, 93, 207, 452, 997, 2176, 4776, 10418, 22781, 49674, 108421
Offset: 1
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)))
Cf.
A000081,
A000108,
A001003,
A005043,
A007562,
A118376,
A143363,
A316470,
A319122,
A319378,
A319380,
A319381.
-
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}]
A319381
Number of plane trees with n nodes where the sequence of branches directly under any given node is a membership-chain.
Original entry on oeis.org
1, 1, 1, 2, 2, 4, 6, 9, 11, 20, 28, 40, 58, 82, 110, 159, 217, 305, 420, 570, 767, 1042
Offset: 1
The a(9) = 11 membership-chain trees:
((((((((o)))))))) (((((((o)o)))))) ((((((o)o)o)))) (((((o)o)o)o))
((((((o))(o))))) (((((o)o)(o)))) ((((o)o)(o)o))
(((((o)))((o)))) (((((o))(o)o))) ((((o))(o)o)o)
((((o))(o))(o))
Cf.
A000081,
A000108,
A001003,
A005043,
A007562,
A118376,
A316470,
A319122,
A319379,
A319380,
A319436.
-
yanplane[n_]:=If[n==1,{{}},Join@@Table[Select[Tuples[yanplane/@c],And@@MemberQ@@@Partition[#,2,1]&],{c,Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[yanplane[n]],{n,10}]
A319378
Number of plane trees with n nodes where the sequence of branches directly under any given node with at least two branches has empty intersection.
Original entry on oeis.org
1, 1, 2, 5, 13, 39, 118, 375, 1225, 4079, 13794, 47287, 163962, 573717, 2023800
Offset: 1
The a(5) = 13 locally nonintersecting plane trees:
((((o)))) (((oo))) ((ooo)) (oooo)
(((o)o)) ((oo)o)
((o(o))) (o(oo))
(((o))o) ((o)oo)
(o((o))) (o(o)o)
(oo(o))
Cf.
A000081,
A000108,
A001003,
A005043,
A007562,
A118376,
A143363,
A316470,
A319122,
A319379,
A319380,
A319381,
A319436.
-
monplane[n_]:=If[n==1,{{}},Join@@Table[Select[Tuples[monplane/@c],Or[Length[#]==1,Intersection@@#=={}]&],{c,Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[monplane[n]],{n,10}]
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