OFFSET
1,2
COMMENTS
A locally disjoint enriched p-tree of weight n is either the number n itself or a finite sequence of non-overlapping locally disjoint enriched p-trees whose weights are weakly decreasing and sum to n.
EXAMPLE
The a(1) = 1 through a(4) = 12 enriched p-trees:
1 2 3 4
(11) (21) (22)
(111) (31)
((11)1) (211)
(1111)
((11)2)
((21)1)
(2(11))
((11)11)
((111)1)
(((11)1)1)
((11)(11))
MATHEMATICA
disjointQ[u_]:=Apply[And, Outer[#1==#2||Intersection[#1, #2]=={}&, u, u, 1], {0, 1}];
ldep[n_]:=Prepend[Select[Join@@Table[Tuples[ldep/@p], {p, Rest[IntegerPartitions[n]]}], disjointQ[DeleteCases[#, _Integer]]&], n];
Table[Length[ldep[n]], {n, 10}]
CROSSREFS
The orderless version is A316696.
The identity case is A331684.
P-trees are A196545.
Enriched p-trees are A289501.
Locally disjoint identity trees are A316471.
Enriched identity p-trees are A331875.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jan 31 2020
STATUS
approved