OFFSET
1,3
COMMENTS
A locally disjoint enriched identity p-tree of weight n is either the number n itself or a finite sequence of distinct non-overlapping locally disjoint enriched identity p-trees whose weights are weakly decreasing and sum to n.
EXAMPLE
The a(1) = 1 through a(6) = 14 enriched p-trees:
1 2 3 4 5 6
(21) (31) (32) (42)
((21)1) (41) (51)
((21)2) (321)
((31)1) ((21)3)
(((21)1)1) ((31)2)
((32)1)
(3(21))
((41)1)
((21)21)
(((21)1)2)
(((21)2)1)
(((31)1)1)
((((21)1)1)1)
MATHEMATICA
disjointQ[u_]:=Apply[And, Outer[#1==#2||Intersection[#1, #2]=={}&, u, u, 1], {0, 1}];
ldeip[n_]:=Prepend[Select[Join@@Table[Tuples[ldeip/@p], {p, Rest[IntegerPartitions[n]]}], UnsameQ@@#&&disjointQ[DeleteCases[#, _Integer]]&], n];
Table[Length[ldeip[n]], {n, 12}]
CROSSREFS
The orderless version is A316694.
The non-identity version is A331687.
Identity trees are A004111.
P-trees are A196545.
Enriched p-trees are A289501.
Locally disjoint identity trees are A316471.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jan 31 2020
STATUS
approved