A083041 Number of symmetric sum-free subsets of {1,2,...,n-1} with sums taken mod n.

1, 2, 1, 3, 3, 4, 4, 8, 4, 14, 11, 14, 16, 31, 19, 45, 37, 56, 55, 106, 55, 164, 122, 179, 190, 353, 178, 467, 379, 648, 541, 1022, 601, 1572, 1171, 1645, 1594, 3238, 1708, 4523, 3220, 5495, 4516, 8694, 5103, 13259, 8948, 14471, 12145, 27156, 13441, 33752, 24155

Offset

1,2

Comments

Parker vector for K_3-free graphs.

References

P. J. Cameron, Portrait of a typical sum-free set, Surveys in combinatorics 1987, London Math. Soc. Lecture Note Ser., 123, 1987, pp. 13-42.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..100

D. A. Gewurz and F. Merola, Sequences realized as Parker vectors of oligomorphic permutation groups, J. Integer Seq., 6 (2003), 03.1.6

Example

a(3) = 1, as {} is the only symmetric sum-free set ({1} is not symmetric, while {1,2} is not sum-free). a(4)=3; its symmetric sum-free subsets are {}, {1,3}, {2}.

Prog

(PARI)
a(n)={
   my(accept(b, k)=for(i=1, k, if(bittest(b, i), if(bittest(b, min(k+i, n-k-i)) || bittest(b, k-i), return(0)))); 1);
   my(recurse(k, b)=if(2*k > n, 1, self()(k+1, b) + if(accept(b + (1<<k), k), self()(k+1, b + (1<<k)))));
   recurse(1, 0);
} \\ Andrew Howroyd, Jan 12 2020

Crossrefs

Cf. A007865.

Sequence in context: A112194 A238788 A350844 * A318611 A366472 A130067

Adjacent sequences: A083038 A083039 A083040 * A083042 A083043 A083044

Keyword

nonn

Author

Daniele A. Gewurz (gewurz(AT)mat.uniroma1.it), Francesca Merola (merola(AT)mat.uniroma1.it), May 06 2003

Extensions

Terms a(32) and beyond from Andrew Howroyd, Jan 12 2020

Status

approved