A083041 - OEIS

%I #12 Jan 12 2020 12:46:06

%S 1,2,1,3,3,4,4,8,4,14,11,14,16,31,19,45,37,56,55,106,55,164,122,179,

%T 190,353,178,467,379,648,541,1022,601,1572,1171,1645,1594,3238,1708,

%U 4523,3220,5495,4516,8694,5103,13259,8948,14471,12145,27156,13441,33752,24155

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

%C Parker vector for K_3-free graphs.

%D 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.

%H Andrew Howroyd, <a href="/A083041/b083041.txt">Table of n, a(n) for n = 1..100</a>

%H D. A. Gewurz and F. Merola, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Gewurz/gewurz5.html">Sequences realized as Parker vectors of oligomorphic permutation groups</a>, J. Integer Seq., 6 (2003), 03.1.6

%e 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}.

%o (PARI)

%o a(n)={

%o    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);

%o    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)))));

%o    recurse(1, 0);

%o } \\ _Andrew Howroyd_, Jan 12 2020

%Y Cf. A007865.

%K nonn

%O 1,2

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

%E Terms a(32) and beyond from _Andrew Howroyd_, Jan 12 2020