From Gus Wiseman, May 17 2019: The a(1) = 1 through a(6) = 17 rulers: {0,1} {0,1,2} {0,1,3} {0,1,2,4} {0,1,2,5} {0,1,4,6} {0,2,3} {0,1,3,4} {0,1,3,5} {0,2,5,6} {0,1,2,3} {0,2,3,4} {0,2,4,5} {0,1,2,3,6} {0,1,2,3,4} {0,3,4,5} {0,1,2,4,6} {0,1,2,3,5} {0,1,2,5,6} {0,1,2,4,5} {0,1,3,4,6} {0,1,3,4,5} {0,1,3,5,6} {0,2,3,4,5} {0,1,4,5,6} {0,1,2,3,4,5} {0,2,3,5,6} {0,2,4,5,6} {0,3,4,5,6} {0,1,2,3,4,6} {0,1,2,3,5,6} {0,1,2,4,5,6} {0,1,3,4,5,6} {0,2,3,4,5,6} {0,1,2,3,4,5,6} The a(1) = 1 through a(6) = 17 compositions are: (1) (11) (12) (112) (113) (132) (21) (121) (122) (231) (111) (211) (221) (1113) (1111) (311) (1122) (1112) (1131) (1121) (1212) (1211) (1221) (2111) (1311) (11111) (2121) (2211) (3111) (11112) (11121) (11211) (12111) (21111) (111111)