
COMMENTS

From Gus Wiseman, May 31 2019: (Start)
A Golomb ruler of length n is a subset of {0...n} containing 0 and n and such that every pair of distinct terms has a different difference. For example, the a(2) = 1 through a(8) = 1 Golomb rulers are:
2: {0,1}
3: {0,1,3}
4: {0,1,4,6}
5: {0,1,4,9,11}
5: {0,2,7,8,11}
6: {0,1,4,10,12,17}
6: {0,1,4,10,15,17}
6: {0,1,8,11,13,17}
6: {0,1,8,12,14,17}
7: {0,1,4,10,18,23,25}
7: {0,1,7,11,20,23,25}
7: {0,2,3,10,16,21,25}
7: {0,2,7,13,21,22,25}
7: {0,1,11,16,19,23,25}
8: {0,1,4,9,15,22,32,34}
Also half the number of length(n  1) compositions of A003022(n) such that every consecutive subsequence has a different sum. For example, the a(2) = 1 through a(8) = 1 compositions are (A = 10):
2: (1)
3: (1,2)
4: (1,3,2)
5: (1,3,5,2)
5: (2,5,1,3)
6: (1,3,6,2,5)
6: (1,3,6,5,2)
6: (1,7,3,2,4)
6: (1,7,4,2,3)
7: (1,3,6,8,5,2)
7: (1,6,4,9,3,2)
7: (2,1,7,6,5,4)
7: (2,5,6,8,1,3)
7: (1,A,5,3,4,2)
8: (1,3,5,6,7,A,2)
(End)
