A382399 Number of subsets of Z_n such that every ordered pair of distinct elements has a different difference.

1, 2, 3, 7, 9, 16, 19, 43, 49, 100, 91, 177, 193, 352, 323, 691, 673, 1242, 1135, 2129, 2041, 3634, 3103, 5843, 5473, 9326, 8139, 16579, 14001, 24796, 21271, 38813, 34369, 60292, 49539, 86451, 81361, 131684, 110391, 196717, 171761, 286878, 236167, 419337, 370569, 618346, 501999, 872415, 763777, 1235438, 1028451

Offset: 0

Author

Andrew Howroyd, Mar 24 2025

Keywords

• nonn

Comments

Arithmetic is done modulo n.

Also the number of subsets of Z_n such that every unordered pair of (not necessarily distinct) elements has a different sum.

Examples

			The a(0) = 1 through a(5) = 16 subsets:
  {}  {}   {}     {}     {}       {}
      {0}  {0}    {0}    {0}      {0}
           {1}    {1}    {1}      {1}
                  {2}    {2}      {2}
                  {0,1}  {3}      {3}
                  {0,2}  {0,1}    {4}
                  {1,2}  {0,3}    {0,1}
                         {1,2}    {0,2}
                         {2,3}    {0,3}
                                  {0,4}
                                  {1,2}
                                  {1,3}
                                  {1,4}
                                  {2,3}
                                  {2,4}
                                  {3,4}
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..80
• Wikipedia, Sidon sequence.
• Index entries for sequences related to Golomb rulers.

Crossrefs

Cf. A143823, A325679, A325681, A382400.

Programs

PARI

a(n)={
   my(recurse(k,r,b,w)=
      if(k >= n, 1,
         b+=1<
				

Formula

a(n) = n*A325681(n) + 1.