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%I #14 Nov 08 2020 09:20:00
%S 1,2,0,3,2,0,4,4,0,0,5,8,2,0,0,6,12,5,0,0,0,7,18,14,2,0,0,0,8,24,24,4,
%T 0,0,0,0,9,32,45,19,2,0,0,0,0,10,40,65,32,3,0,0,0,0,0,11,50,100,72,17,
%U 2,0,0,0,0,0,12,60,137,121,35,3,0,0,0,0,0,0
%N Triangle read by rows: T(n,k) is the number of sum-free subsets of {1..n} with cardinality k for 1 <= k <= n.
%H Fausto A. C. Cariboni, <a href="/A338737/b338737.txt">Rows n = 1..70, flattened</a>
%e The 8 sum-free subsets of {1,2,3,4} with at least one element are {1}, {2}, {3}, {4}, {1,3}, {1,4}, {2,3}, {3,4}, hence the 4th row is 4,4,0,0.
%e The triangle begins:
%e 1;
%e 2, 0;
%e 3, 2, 0;
%e 4, 4, 0, 0;
%e 5, 8, 2, 0, 0;
%e ...
%o (PARI) sumfree(v) = {for(i=1, #v, for (j=1, i, if (setsearch(v, v[i]+v[j]), return (0)););); return (1);}
%o row(n) = {my(v = vector(n)); forsubset(n, s, if (#s && sumfree(Set(s)), v[#s]++);); v;} \\ _Michel Marcus_, Nov 08 2020
%Y Cf. A007865, A288887, A288888.
%K nonn,tabl
%O 1,2
%A _Fausto A. C. Cariboni_, Nov 05 2020
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