This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A325684 #11 Feb 27 2022 05:46:02
%S A325684 1,1,1,2,3,4,5,12,12,24,40,46,92,133,192,308,546,710,1108,1754,2726,
%T A325684 3878,5928,9260,14238,20502,30812,48378,72232,105744,160308,241592,
%U A325684 362348,540362,797750,1183984,1786714
%N A325684 Number of minimal complete rulers of length n.
%C A325684 A complete ruler of length n is a subset of {0..n} containing 0 and n and such that the differences of distinct terms (up to sign) cover an initial interval of positive integers.
%C A325684 Also the number of maximal (most coarse) compositions of n whose consecutive subsequence-sums cover an initial interval of positive integers.
%e A325684 The a(1) = 1 through a(7) = 12 rulers:
%e A325684 {0,1} {0,1,2} {0,1,3} {0,1,2,4} {0,1,2,5} {0,1,4,6} {0,1,2,3,7}
%e A325684 {0,2,3} {0,1,3,4} {0,1,3,5} {0,2,5,6} {0,1,2,4,7}
%e A325684 {0,2,3,4} {0,2,4,5} {0,1,2,3,6} {0,1,2,5,7}
%e A325684 {0,3,4,5} {0,1,3,5,6} {0,1,3,5,7}
%e A325684 {0,3,4,5,6} {0,1,3,6,7}
%e A325684 {0,1,4,5,7}
%e A325684 {0,1,4,6,7}
%e A325684 {0,2,3,6,7}
%e A325684 {0,2,4,6,7}
%e A325684 {0,2,5,6,7}
%e A325684 {0,3,5,6,7}
%e A325684 {0,4,5,6,7}
%e A325684 The a(1) = 1 through a(9) = 24 compositions:
%e A325684 (1) (11) (12) (112) (113) (132) (1114) (1133) (1143)
%e A325684 (21) (121) (122) (231) (1123) (1241) (1332)
%e A325684 (211) (221) (1113) (1132) (1322) (2331)
%e A325684 (311) (1221) (1222) (1412) (3411)
%e A325684 (3111) (1231) (1421) (11115)
%e A325684 (1312) (2141) (11124)
%e A325684 (1321) (2231) (11142)
%e A325684 (2131) (3311) (11241)
%e A325684 (2221) (11114) (11322)
%e A325684 (2311) (11132) (12141)
%e A325684 (3211) (23111) (12222)
%e A325684 (4111) (41111) (12231)
%e A325684 (12312)
%e A325684 (13221)
%e A325684 (14112)
%e A325684 (14121)
%e A325684 (14211)
%e A325684 (21141)
%e A325684 (21321)
%e A325684 (22221)
%e A325684 (22311)
%e A325684 (24111)
%e A325684 (42111)
%e A325684 (51111)
%t A325684 fasmin[y_]:=Complement[y,Union@@Table[Union[s,#]&/@Rest[Subsets[Complement[Union@@y,s]]],{s,y}]];
%t A325684 Table[Length[fasmin[Accumulate/@Select[Join@@Permutations/@IntegerPartitions[n],SubsetQ[ReplaceList[#,{___,s__,___}:>Plus[s]],Range[n]]&]]],{n,0,15}]
%Y A325684 Cf. A000079, A103295, A126796, A143823, A169942, A325677, A325683, A325685.
%K A325684 nonn,more
%O A325684 0,4
%A A325684 _Gus Wiseman_, May 13 2019
%E A325684 a(16)-a(36) from _Fausto A. C. Cariboni_, Feb 27 2022