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%I #13 Jul 06 2022 17:43:27
%S 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,
%T 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,
%U 11,53,143,234,238,149,55,11,1,1,12,64,196,377,472,387,204,66,12,1
%N 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).
%C S is product-free if for any i,j in S, not necessarily distinct, i*j is not in S.
%C For n >= 2, the alternating row sums give 0.
%H Marcel K. Goh and Jonah Saks, <a href="https://arxiv.org/abs/2206.12535">Alternating-sum statistics for certain sets of integers</a>, arXiv:2206.12535 [math.CO], 2022.
%e Triangle T(n,k) begins:
%e n/k 0 1 2 3 4 5 6 7 8 9
%e 0 1
%e 1 1
%e 2 1 1
%e 3 1 2 1
%e 4 1 3 2
%e 5 1 4 5 2
%e 6 1 5 9 6 1
%e 7 1 6 14 15 7 1
%e 8 1 7 20 29 22 8 1
%e 9 1 8 26 43 38 17 3
%e 10 1 9 34 68 76 47 15 2
%e 11 1 10 43 102 144 123 62 17 2
%e 12 1 11 53 143 234 238 149 55 11 1
%e ...
%e For n=5 and k=3 the T(5,3) = 2 sets are {2,3,5} and {3,4,5}.
%Y Row sums give A326489.
%Y Cf. A028391.
%K nonn,tabf
%O 0,6
%A _Marcel K. Goh_, Jun 28 2022
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