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A355146
Triangle read by rows: T(n,k) is the number of subsets of {1,...,n} of cardinality k in which every pair of elements is coprime; n >= 0, 0 <= k <= A036234(n).
1
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 5, 2, 1, 5, 9, 7, 2, 1, 6, 11, 8, 2, 1, 7, 17, 19, 10, 2, 1, 8, 21, 25, 14, 3, 1, 9, 27, 37, 24, 6, 1, 10, 31, 42, 26, 6, 1, 11, 41, 73, 68, 32, 6, 1, 12, 45, 79, 72, 33, 6, 1, 13, 57, 124, 151, 105, 39, 6, 1, 14, 63, 138, 167, 114, 41, 6
OFFSET
0,5
COMMENTS
For n >= 1, the alternating row sums equal 0.
LINKS
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
0 1
1 1 1
2 1 2 1
3 1 3 3 1
4 1 4 5 2
5 1 5 9 7 2
6 1 6 11 8 2
7 1 7 17 19 10 2
8 1 8 21 25 14 3
9 1 9 27 37 24 6
10 1 10 31 42 26 6
11 1 11 41 73 68 32 6
12 1 12 45 79 72 33 6
...
For n=8 and k=5 the T(8,5)=3 sets are {1,2,3,5,7}, {1,3,4,5,7}, and {1,3,5,7,8}.
CROSSREFS
Row sums give A084422.
Sequence in context: A099573 A107430 A330885 * A255741 A132892 A174448
KEYWORD
nonn,tabf
AUTHOR
Marcel K. Goh, Jun 27 2022
STATUS
approved