A300352 Number of strict trees of weight n with distinct leaves.

1, 1, 2, 2, 3, 6, 8, 11, 17, 40, 48, 76, 109, 159, 400, 470, 745, 1057, 1576, 2103, 5267, 6022, 9746, 13390, 20099, 26542, 39396, 82074, 101387, 152291, 215676, 308937, 423587, 596511, 799022, 1623311, 1960223, 2947722, 4048704, 5845982, 7794809, 11028888

Offset

1,3

Comments

A strict tree of weight n > 0 is either a single node of weight n, or a sequence of two or more strict trees with strictly decreasing weights summing to n.

Links

Table of n, a(n) for n=1..42.

Formula

a(n) = Sum_{i=1..A000009(n)} A294018(A246867(n,i)).

Example

The a(8) = 11 strict trees with distinct leaves: 8, (71), ((52)1), ((43)1), (62), ((51)2), (53), ((41)3), (5(21)), (521), (431).

Mathematica

sps[{}]:={{}}; sps[set:{i_, ___}]:=
Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
str[q_]:=str[q]=If[Length[q]===1, 1, Total[Times@@@Map[str, Select[sps[q], And[Length[#]>1, UnsameQ@@Total/@#]&], {2}]]];
Table[Total[str/@Select[IntegerPartitions[n], UnsameQ@@#&]], {n, 1, 20}]

Crossrefs

Cf. A000009, A056239, A063834, A196545, A246867, A273873, A281145, A289501, A294018, A294079, A296150, A299201, A299202, A299203, A300353, A300354, A300355.

Sequence in context: A193595 A077871 A215450 * A035587 A039870 A100948

Adjacent sequences: A300349 A300350 A300351 * A300353 A300354 A300355

Keyword

nonn

Author

Gus Wiseman, Mar 03 2018

Status

approved