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A294150 Number of knapsack partitions of n that are also knapsack factorizations. 3
1, 1, 1, 2, 2, 4, 4, 6, 8, 10, 12, 13, 20, 20, 29, 30, 41, 41, 56, 53, 81, 75 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n) is the number of finite multisets of positive integers summing to n such that every distinct submultiset has a different sum, and also every distinct submultiset has a different product.

LINKS

Table of n, a(n) for n=1..22.

R. Ehrenborg and M. Readdy, The Mobius function of partitions with restricted block sizes, Advances in Applied Mathematics, Volume 39, Issue 3, September 2007, Pages 283-292.

EXAMPLE

The a(12) = 13 partitions are:

(12),

(10 2), (9 3), (8 4), (7 5), (6 6),

(8 2 2), (7 3 2), (5 5 2), (5 4 3), (4 4 4),

(3 3 3 3),

(2 2 2 2 2 2).

MATHEMATICA

nn=22;

dubQ[y_]:=And[UnsameQ@@Times@@@Union[Rest@Subsets[y]], UnsameQ@@Plus@@@Union[Rest@Subsets[y]]];

Table[Length@Select[IntegerPartitions[n], dubQ], {n, nn}]

CROSSREFS

Cf. A000041, A001055, A108917, A275972, A292886, A293627.

Sequence in context: A183002 A211859 A057601 * A087135 A227135 A162417

Adjacent sequences:  A294147 A294148 A294149 * A294151 A294152 A294153

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Oct 23 2017

STATUS

approved

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Last modified March 23 18:13 EDT 2019. Contains 321433 sequences. (Running on oeis4.)