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A288887 Triangle read by rows: T(n,k) is the number of times k is a member of a sum-free subset of {1, ..., n} for 1 <= k <= n.

%I A288887 #30 Feb 16 2025 08:33:48
%S A288887 1,1,1,2,2,3,3,2,4,3,5,3,7,5,7,7,5,7,8,10,8,12,8,12,13,17,13,18,16,13,
%T A288887 17,13,23,18,25,19,28,21,30,21,40,32,43,32,47,37,29,40,29,40,45,57,45,
%U A288887 63,43,62,44,66,45,65,72,95,71,104,70,102,85,66,95,71,89,72,132,109,139,104,142,116
%N A288887 Triangle read by rows: T(n,k) is the number of times k is a member of a sum-free subset of {1, ..., n} for 1 <= k <= n.
%H A288887 Fausto A. C. Cariboni, <a href="/A288887/b288887.txt">Rows n = 1..70, flattened</a>
%H A288887 Ben Burns, <a href="/A288887/a288887.cs.txt">C# program to generate a(n) up to n=64</a>
%H A288887 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Sum-FreeSet.html">Sum-Free Set</a>
%e A288887 For the nine sum-free subsets of {1,2,3,4}, 1 is a member of three of them, 2 is a member of two, 3 is a member of four, and 4 is a member of three, hence the 4th row is 3,2,4,3.
%e A288887 The triangle begins:
%e A288887    1;
%e A288887    1,  1;
%e A288887    2,  2,  3;
%e A288887    3,  2,  4,  3;
%e A288887    5,  3,  7,  5,  7;
%e A288887    7,  5,  7,  8, 10,  8;
%e A288887   12,  8, 12, 13, 17, 13, 18;
%e A288887   16, 13, 17, 13, 23, 18, 25, 19;
%e A288887   ...
%o A288887 (PARI) sumfree(v) = {for(i=1, #v, for (j=1, i, if (setsearch(v, v[i]+v[j]), return (0)););); return (1);}
%o A288887 row(n) = {my(v = vector(n)); forsubset(n, s, if (sumfree(Set(s)), for (k=1, n, if (setsearch(Set(s), k), v[k]++);););); v;} \\ _Michel Marcus_, Nov 08 2020
%Y A288887 Cf. A007865, A288888 (row sums).
%K A288887 nonn,tabl
%O A288887 1,4
%A A288887 _Ben Burns_, Jun 18 2017