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A325880
Number of maximal subsets of {1..n} containing n such that every ordered pair of distinct elements has a different difference.
10
1, 1, 2, 2, 4, 8, 8, 10, 18, 34, 50, 70, 78, 89, 120, 181, 277, 401, 561, 728, 867, 1031, 1219, 1537, 2013, 2684, 3581, 4973, 6435, 8124, 9974, 12054, 14057, 16890, 19783, 24102, 29539, 37247, 46301, 59825, 74556, 94064, 115057, 141068, 167521, 200790, 232798, 273734
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
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 02 2019
EXTENSIONS
a(25) onwards from Andrew Howroyd, Mar 23 2025
STATUS
approved