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A338737
Triangle read by rows: T(n,k) is the number of sum-free subsets of {1..n} with cardinality k for 1 <= k <= n.
1
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, 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, 2, 0, 0, 0, 0, 0, 12, 60, 137, 121, 35, 3, 0, 0, 0, 0, 0, 0
OFFSET
1,2
LINKS
Fausto A. C. Cariboni, Rows n = 1..70, flattened
EXAMPLE
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.
The triangle begins:
1;
2, 0;
3, 2, 0;
4, 4, 0, 0;
5, 8, 2, 0, 0;
...
PROG
(PARI) sumfree(v) = {for(i=1, #v, for (j=1, i, if (setsearch(v, v[i]+v[j]), return (0)); ); ); return (1); }
row(n) = {my(v = vector(n)); forsubset(n, s, if (#s && sumfree(Set(s)), v[#s]++); ); v; } \\ Michel Marcus, Nov 08 2020
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved