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A294018 Number of strict trees whose leaves are the parts of the integer partition with Heinz number n. 7
0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 3, 1, 0, 1, 1, 1, 3, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 0, 1, 4, 1, 1, 1, 3, 1, 6, 1, 1, 1, 1, 1, 4, 1, 1, 0, 1, 1, 8, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 4, 1, 1, 4, 1, 1, 6, 1, 4, 1, 1, 1, 4, 1, 1, 1, 1, 1, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,30
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
FORMULA
A273873(n) = Sum_{i=1..A000041(n)} a(A215366(n,i)).
EXAMPLE
The a(84) = 8 strict trees: (((42)1)1), (((41)2)1), ((4(21))1), ((421)1), (((41)1)2), ((41)(21)), ((41)21), (4(21)1).
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, UnsameQ@@Total/@#]&]}]];
qci/@ptns
CROSSREFS
Sequence in context: A121383 A194521 A181434 * A355692 A192003 A226873
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 06 2018
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)