cp's OEIS Frontend

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].

%I A360285 #18 Oct 23 2023 17:39:36
%S A360285 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,
%T A360285 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,
%U A360285 39,36,21,7,1,1,15,34,48,41,22,7,1,1,16,41,69,76,57,28,8,1
%N 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].
%H A360285 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 A360285 Triangle T(n,k) begins:
%e A360285    n/k 0  1  2  3  4 5 6
%e A360285    0   1
%e A360285    1   1  1
%e A360285    2   1  2
%e A360285    3   1  3
%e A360285    4   1  4  1
%e A360285    5   1  5  1
%e A360285    6   1  6  4  1
%e A360285    7   1  7  4  1
%e A360285    8   1  8  7  4  1
%e A360285    9   1  9  9  5  1
%e A360285   10   1 10 14 11  5 1
%e A360285   11   1 11 14 11  5 1
%e A360285   12   1 12 21 24 16 6 1
%e A360285   ...
%e A360285 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}.
%Y A360285 Cf. A056171, A355146.
%K A360285 nonn,tabf
%O A360285 0,5
%A A360285 _Marcel K. Goh_, Feb 01 2023