A299203 - OEIS

A299203

Number of enriched p-trees whose multiset of leaves is the integer partition with Heinz number n.

0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 5, 1, 3, 1, 3, 1, 1, 1, 11, 1, 1, 2, 3, 1, 5, 1, 12, 1, 1, 1, 15, 1, 1, 1, 11, 1, 4, 1, 3, 3, 1, 1, 38, 1, 3, 1, 3, 1, 9, 1, 9, 1, 1, 1, 21, 1, 1, 4, 34, 1, 4, 1, 3, 1, 5, 1, 54, 1, 1, 3, 3, 1, 4, 1, 33, 5, 1, 1, 23, 1, 1, 1, 9, 1, 20, 1, 3, 1, 1, 1, 117, 1, 3, 3, 12, 1, 4, 1, 9, 4, 1, 1, 57, 1, 4, 1, 34

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OFFSET

1,8

COMMENTS

By convention, a(1) = 0.

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

LINKS

Table of n, a(n) for n=1..112.

EXAMPLE

a(54) = 9: (((22)2)1), ((222)1), (((22)1)2), (((21)2)2), ((221)2), ((22)(21)), ((22)21), ((21)22), (2221).

a(40) = 11: ((31)(11)), (((31)1)1), ((3(11))1), ((311)1), (3((11)1)), (3(111)), (((11)1)3), ((111)3), ((31)11), (3(11)1), (3111).

a(36) = 15: ((22)(11)), ((2(11))2), (((11)2)2), (((21)1)2), ((211)2), (((22)1)1), (((21)2)1), ((221)1), ((21)(21)), (22(11)), (2(11)2), ((11)22), ((22)11), ((21)21), (2211).

MATHEMATICA

nn=120;

ptns=Table[If[n===1, {}, Join@@Cases[FactorInteger[n]//Reverse, {p_, k_}:>Table[PrimePi[p], {k}]]], {n, nn}];

tris=Join@@Map[Tuples[IntegerPartitions/@#]&, ptns];

qci[y_]:=qci[y]=If[Length[y]===1, 1, Sum[Times@@qci/@t, {t, Select[tris, And[Length[#]>1, Sort[Join@@#, Greater]===y]&]}]];

qci/@ptns

CROSSREFS

Cf. A000041, A063834, A112798, A196545, A273873, A281145, A289501, A290261, A296150, A299200, A299201, A299202.

Sequence in context: A174726 A300239 A354364 * A329036 A205552 A255707

Adjacent sequences: A299200 A299201 A299202 * A299204 A299205 A299206

KEYWORD

nonn

AUTHOR

Gus Wiseman, Feb 05 2018

STATUS

approved