A382398 Number of maximum sized subsets of {1..n} such that every pair of distinct elements has a different sum.

1, 1, 1, 1, 4, 2, 8, 22, 2, 14, 40, 102, 214, 4, 24, 92, 236, 564, 1148, 4, 18, 90, 270, 694, 1558, 2, 6, 24, 76, 252, 632, 1554, 3282, 6820, 12942, 6, 24, 84, 246, 664, 1562, 3442, 7084, 14336, 27202, 50520, 2, 26, 88, 294, 704, 1716, 3708, 8028, 16108, 31466, 58320, 107136, 4, 20, 54

Offset: 0

Author

Andrew Howroyd, Mar 23 2025

Keywords

• nonn

Examples

			The a(1) = 1 through a(6) = 8 subsets:
  {1}  {1,2}  {1,2,3}  {1,2,3}  {1,2,3,5}  {1,2,3,5}
                       {1,2,4}  {1,3,4,5}  {1,2,3,6}
                       {1,3,4}             {1,2,4,6}
                       {2,3,4}             {1,3,4,5}
                                           {1,3,5,6}
                                           {1,4,5,6}
                                           {2,3,4,6}
                                           {2,4,5,6}
Compare the above examples with A325878.
		

Crossrefs

Cf. A039836 (maximum size), A196723, A325878, A382395.

Programs

PARI

a(n)={
   local(best,count);
   my(recurse(k,r,b,w)=
      if(k > n, if(r>=best, if(r>n,best=r;count=0); count++),
         self()(k+1, r, b, w);
         if(!bitand(w,b<