A382400 Number of subsets of Z_n such that every ordered pair of distinct elements has a different sum.

1, 2, 4, 8, 15, 26, 48, 78, 133, 202, 316, 474, 755, 1054, 1604, 2196, 3305, 4370, 6208, 8228, 11631, 15086, 20912, 26842, 37581, 46626, 64052, 79984, 109635, 133314, 176156, 217094, 291409, 343872, 457828, 547576, 718375, 852074, 1112128, 1308230, 1714741

Offset: 0

Author

Andrew Howroyd, Mar 27 2025

Keywords

• nonn

Comments

Arithmetic is done modulo n.

Every subset of size at most 3 is included. The cake numbers A000125 give the number of such subsets.

Examples

			The a(6) = 48 subsets are 42 subsets of size at most 3 and the following 6: {1,3,4,5}, {1,2,3,5}, {0,2,4,5}, {0,2,3,4}, {0,1,3,5}, {0,1,2,4}. Each of the size 4 subsets is perfect in the sense that every number from 0..5 can be written as the sum of two elements modulo 6 in exactly one way.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A000125, A196723, A382399.

Programs

PARI

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