A331687 Number of locally disjoint enriched p-trees of weight n.

1, 2, 4, 12, 29, 93, 249, 803, 2337, 7480, 23130, 77372, 247598, 834507, 2762222

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.

Links

Table of n, a(n) for n=1..15.

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.

Cf. A000669, A141268, A316473, A316495, A316694, A316697, A319312, A331678, A331679, A331680, A331686, A331871, A331874.

Sequence in context: A148179 A148180 A148181 * A148182 A148183 A148184

Adjacent sequences: A331684 A331685 A331686 * A331688 A331689 A331690

Keyword

nonn,more

Author

Gus Wiseman, Jan 31 2020

Status

approved