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A355147 Triangle read by rows: T(n,k) is the number of product-free subsets of {1,...,n} with cardinality k; n >= 0, 0 <= k <= A028391(n). 0
1, 1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 4, 5, 2, 1, 5, 9, 6, 1, 1, 6, 14, 15, 7, 1, 1, 7, 20, 29, 22, 8, 1, 1, 8, 26, 43, 38, 17, 3, 1, 9, 34, 68, 76, 47, 15, 2, 1, 10, 43, 102, 144, 123, 62, 17, 2, 1, 11, 53, 143, 234, 238, 149, 55, 11, 1, 1, 12, 64, 196, 377, 472, 387, 204, 66, 12, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

S is product-free if for any i,j in S, not necessarily distinct, i*j is not in S.

For n >= 2, the alternating row sums give 0.

LINKS

Table of n, a(n) for n=0..76.

Marcel K. Goh and Jonah Saks, Alternating-sum statistics for certain sets of integers, arXiv:2206.12535 [math.CO], 2022.

EXAMPLE

Triangle T(n,k) begins:

  n/k 0  1  2   3   4   5   6  7  8 9

   0  1

   1  1

   2  1  1

   3  1  2  1

   4  1  3  2

   5  1  4  5   2

   6  1  5  9   6   1

   7  1  6 14  15   7   1

   8  1  7 20  29  22   8   1

   9  1  8 26  43  38  17   3

  10  1  9 34  68  76  47  15  2

  11  1 10 43 102 144 123  62 17  2

  12  1 11 53 143 234 238 149 55 11 1

  ...

For n=5 and k=3 the T(5,3) = 2 sets are {2,3,5} and {3,4,5}.

CROSSREFS

Row sums give A326489.

Cf. A028391.

Sequence in context: A348445 A023996 A307998 * A049998 A029253 A288165

Adjacent sequences:  A355144 A355145 A355146 * A355149 A355150 A355151

KEYWORD

nonn,tabf

AUTHOR

Marcel K. Goh, Jun 28 2022

STATUS

approved

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Last modified August 14 17:12 EDT 2022. Contains 356122 sequences. (Running on oeis4.)