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A319271
Number of series-reduced locally non-intersecting aperiodic rooted trees with n nodes.
2
1, 1, 0, 1, 1, 3, 3, 9, 12, 27, 42, 91, 151, 312, 550, 1099, 2026, 3999, 7527, 14804, 28336, 55641, 107737, 211851, 413508, 814971, 1600512, 3162761, 6241234
OFFSET
1,6
COMMENTS
A rooted tree is series-reduced if every non-leaf node has at least two branches, and aperiodic if the multiplicities in the multiset of branches directly under any given node are relatively prime, and locally non-intersecting if the branches directly under any given node with more than one branch have empty intersection.
EXAMPLE
The a(8) = 9 rooted trees:
(o(o(o(o))))
(o(o(o)(o)))
(o(ooo(o)))
(oo(oo(o)))
(o(o)(o(o)))
(ooo(o(o)))
(o(o)(o)(o))
(ooo(o)(o))
(ooooo(o))
MATHEMATICA
btrut[n_]:=btrut[n]=If[n===1, {{}}, Select[Join@@Function[c, Union[Sort/@Tuples[btrut/@c]]]/@IntegerPartitions[n-1], And[Intersection@@#=={}, GCD@@Length/@Split[#]==1]&]];
Table[Length[btrut[n]], {n, 30}]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 16 2018
STATUS
approved