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A083041 Number of symmetric sum-free subsets of {1,2,...,n-1} with sums taken mod n. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A027157 A112194 A238788 * A318611 A130067 A282906

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

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Last modified April 17 11:50 EDT 2021. Contains 343064 sequences. (Running on oeis4.)