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A360285 Triangle read by rows: T(n,k) is the number of subsets of {1,...,n} of cardinality k in which no two elements are coprime; n >= 0, 0 <= k <= floor(n/2) + [n=1]. 0
1, 1, 1, 1, 2, 1, 3, 1, 4, 1, 1, 5, 1, 1, 6, 4, 1, 1, 7, 4, 1, 1, 8, 7, 4, 1, 1, 9, 9, 5, 1, 1, 10, 14, 11, 5, 1, 1, 11, 14, 11, 5, 1, 1, 12, 21, 24, 16, 6, 1, 1, 13, 21, 24, 16, 6, 1, 1, 14, 28, 39, 36, 21, 7, 1, 1, 15, 34, 48, 41, 22, 7, 1, 1, 16, 41, 69, 76, 57, 28, 8, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
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
3 1 3
4 1 4 1
5 1 5 1
6 1 6 4 1
7 1 7 4 1
8 1 8 7 4 1
9 1 9 9 5 1
10 1 10 14 11 5 1
11 1 11 14 11 5 1
12 1 12 21 24 16 6 1
...
For n=8 and k=3 the T(8,3)=4 sets are {2,4,6}, {2,4,8}, {2,6,8}, and {4,6,8}.
CROSSREFS
Sequence in context: A195837 A123539 A142593 * A226248 A102547 A305556
KEYWORD
nonn,tabf
AUTHOR
Marcel K. Goh, Feb 01 2023
STATUS
approved

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Last modified March 3 20:15 EST 2024. Contains 370512 sequences. (Running on oeis4.)