A331687 - OEIS

%I #5 Feb 01 2020 14:39:52

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

%N Number of locally disjoint enriched p-trees of weight n.

%C 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.

%e The a(1) = 1 through a(4) = 12 enriched p-trees:

%e   1  2     3        4

%e      (11)  (21)     (22)

%e            (111)    (31)

%e            ((11)1)  (211)

%e                     (1111)

%e                     ((11)2)

%e                     ((21)1)

%e                     (2(11))

%e                     ((11)11)

%e                     ((111)1)

%e                     (((11)1)1)

%e                     ((11)(11))

%t disjointQ[u_]:=Apply[And,Outer[#1==#2||Intersection[#1,#2]=={}&,u,u,1],{0,1}];

%t ldep[n_]:=Prepend[Select[Join@@Table[Tuples[ldep/@p],{p,Rest[IntegerPartitions[n]]}],disjointQ[DeleteCases[#,_Integer]]&],n];

%t Table[Length[ldep[n]],{n,10}]

%Y The orderless version is A316696.

%Y The identity case is A331684.

%Y P-trees are A196545.

%Y Enriched p-trees are A289501.

%Y Locally disjoint identity trees are A316471.

%Y Enriched identity p-trees are A331875.

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

%K nonn,more

%O 1,2

%A _Gus Wiseman_, Jan 31 2020