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, 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

Cf. A007865, A288887, A288888.

Sequence in context: A127479 A284124 A187637 * A141432 A115241 A342238

Adjacent sequences: A338734 A338735 A338736 * A338738 A338739 A338740

Keyword

nonn,tabl

Author

Fausto A. C. Cariboni, Nov 05 2020

Status

approved