OFFSET
1,3
COMMENTS
Also the number of maximal subsets of {1..n} containing n such that every orderless pair of (not necessarily distinct) elements has a different sum.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..60
EXAMPLE
The a(2) = 1 through a(9) = 18 subsets:
{1,2} {1,3} {1,2,4} {1,2,5} {1,2,6} {2,3,7} {3,5,8} {4,6,9}
{2,3} {1,3,4} {1,4,5} {1,3,6} {2,4,7} {4,5,8} {5,6,9}
{2,3,5} {1,4,6} {2,6,7} {1,2,4,8} {1,2,4,9}
{2,4,5} {1,5,6} {3,4,7} {1,2,6,8} {1,2,6,9}
{2,3,6} {4,5,7} {1,3,4,8} {1,2,7,9}
{2,5,6} {4,6,7} {1,3,7,8} {1,3,4,9}
{3,4,6} {1,2,5,7} {1,5,6,8} {1,3,8,9}
{3,5,6} {1,3,6,7} {1,5,7,8} {1,4,8,9}
{2,3,6,8} {1,6,7,9}
{2,4,7,8} {1,6,8,9}
{2,3,5,9}
{2,3,7,9}
{2,4,5,9}
{2,4,8,9}
{2,6,7,9}
{2,6,8,9}
{3,4,7,9}
{3,5,8,9}
MATHEMATICA
fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]], MemberQ[#, n]&&UnsameQ@@Subtract@@@Subsets[Union[#], {2}]&]]], {n, 0, 10}]
PROG
(PARI)
a(n)={
my(ismaxl(b, w)=for(k=1, n, if(!bittest(b, k) && !bitand(w, bitor(b, 1<<k)<<k), return(0))); 1);
my(recurse(k, b, w)=
if(k >= n, ismaxl(b, w),
my(s=self()(k+1, b, w));
b+=1<<k; if(!bitand(w, b<<k), s+=self()(k+1, b, w + (b<<k)));
s);
);
recurse(1, 1<<n, 1<<(2*n));
} \\ Andrew Howroyd, Mar 23 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 02 2019
EXTENSIONS
a(25) onwards from Andrew Howroyd, Mar 23 2025
STATUS
approved