A331684 Number of locally disjoint enriched identity p-trees of weight n.

1, 1, 2, 3, 6, 14, 30, 68, 157, 379, 901, 2229, 5488, 13846, 34801, 89368, 228186, 592943, 1533511, 4026833

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.

Links

Table of n, a(n) for n=1..20.

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.

Enriched identity p-trees are A331875, with locally disjoint case A331687.

Cf. A000669, A005804, A141268, A300660, A316696, A316697, A331678, A331679, A331680, A331683, A331686, A331783, A331874.

Sequence in context: A087293 A250022 A240749 * A106364 A211931 A264078

Adjacent sequences: A331681 A331682 A331683 * A331685 A331686 A331687

Keyword

nonn,more

Author

Gus Wiseman, Jan 31 2020

Status

approved