|
|
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
|
|
|
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);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Daniele A. Gewurz (gewurz(AT)mat.uniroma1.it), Francesca Merola (merola(AT)mat.uniroma1.it), May 06 2003
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|