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 A325684 Number of minimal complete rulers of length n. 11
 1, 1, 1, 2, 3, 4, 5, 12, 12, 24, 40, 46, 92, 133, 192, 308, 546, 710, 1108, 1754, 2726, 3878, 5928, 9260, 14238, 20502, 30812, 48378, 72232, 105744, 160308, 241592, 362348, 540362, 797750, 1183984, 1786714 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS 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. Also the number of maximal (most coarse) compositions of n whose consecutive subsequence-sums cover an initial interval of positive integers. LINKS EXAMPLE The a(1) = 1 through a(7) = 12 rulers: {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} {0,2,3} {0,1,3,4} {0,1,3,5} {0,2,5,6} {0,1,2,4,7} {0,2,3,4} {0,2,4,5} {0,1,2,3,6} {0,1,2,5,7} {0,3,4,5} {0,1,3,5,6} {0,1,3,5,7} {0,3,4,5,6} {0,1,3,6,7} {0,1,4,5,7} {0,1,4,6,7} {0,2,3,6,7} {0,2,4,6,7} {0,2,5,6,7} {0,3,5,6,7} {0,4,5,6,7} The a(1) = 1 through a(9) = 24 compositions: (1) (11) (12) (112) (113) (132) (1114) (1133) (1143) (21) (121) (122) (231) (1123) (1241) (1332) (211) (221) (1113) (1132) (1322) (2331) (311) (1221) (1222) (1412) (3411) (3111) (1231) (1421) (11115) (1312) (2141) (11124) (1321) (2231) (11142) (2131) (3311) (11241) (2221) (11114) (11322) (2311) (11132) (12141) (3211) (23111) (12222) (4111) (41111) (12231) (12312) (13221) (14112) (14121) (14211) (21141) (21321) (22221) (22311) (24111) (42111) (51111) MATHEMATICA fasmin[y_]:=Complement[y, Union@@Table[Union[s, #]&/@Rest[Subsets[Complement[Union@@y, s]]], {s, y}]]; Table[Length[fasmin[Accumulate/@Select[Join@@Permutations/@IntegerPartitions[n], SubsetQ[ReplaceList[#, {___, s__, ___}:>Plus[s]], Range[n]]&]]], {n, 0, 15}] CROSSREFS Cf. A000079, A103295, A126796, A143823, A169942, A325677, A325683, A325685. Sequence in context: A193679 A066574 A240304 * A339453 A281597 A039007 Adjacent sequences: A325681 A325682 A325683 * A325685 A325686 A325687 KEYWORD nonn,more AUTHOR Gus Wiseman, May 13 2019 EXTENSIONS a(16)-a(36) from Fausto A. C. Cariboni, Feb 27 2022 STATUS approved

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Last modified November 27 03:04 EST 2022. Contains 358362 sequences. (Running on oeis4.)