A382396 Number of minimum sized maximal subsets of {1..n} such that every pair of distinct elements has a different difference.

1, 1, 1, 3, 1, 6, 14, 18, 14, 10, 4, 110, 172, 216, 226, 214, 184, 152, 116, 82, 50, 26, 10, 3696, 3904, 3942, 3768, 3504, 3016, 2548, 2060, 1598, 1170, 832, 538, 330, 196, 106, 52, 20, 10, 4, 2, 69610, 62594, 55294, 47610, 40502, 33538, 27254, 21544, 16764, 12676, 9258, 6534, 4516, 3042, 1990, 1254, 754, 448

Offset: 0

Author

Andrew Howroyd, Mar 23 2025

Keywords

• nonn

Comments

Also the number of minimum sized maximal subsets of {1..n} such that every pair of (not necessarily distinct) elements has a different sum.

Examples

			The a(0) = 1 set is {}.
The a(1) = 1 set is {1}.
The a(2) = 1 set is {1,2}.
The a(3) = 3 sets: {1,2}, {1,3}, {2,3}.
The a(11) = 4 sets: {1,2,4,8}, {1,2,4,9}, {1,2,4,10}, {1,2,4,11}.
The a(42) = 2 sets: {10,18,19,25,30}, {13,18,24,25,33}.
See also the examples in A325879.
		

Links

• Wikipedia, Sidon sequence.
• Index entries for sequences related to Golomb rulers.

Crossrefs

Cf. A143823, A325879, A377419, A382395, A382397 (minimum size of set).

Programs

PARI

a(n)={
  local(best,count); best=n+1;
  my(ismaxl(b,w)=for(k=1, n, if(!bittest(b,k) && !bitand(w,bitor(b,1< n, if(ismaxl(b,w),if(r