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 A325685 Number of compositions of n whose distinct consecutive subsequences have different sums, and such that these sums cover an initial interval of positive integers. 10
 1, 1, 1, 3, 1, 5, 3, 5, 3, 9, 1, 9, 5, 7, 5, 11, 1, 13, 5, 9, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A composition of n is a finite sequence of positive integers summing to n. Compare to the definition of perfect partitions (A002033). LINKS EXAMPLE The distinct consecutive subsequences of (3,4,1,1) together with their sums are:    1: {1}    2: {1,1}    3: {3}    4: {4}    5: {4,1}    6: {4,1,1}    7: {3,4}    8: {3,4,1}    9: {3,4,1,1} Because the sums are all different and cover {1...9}, it follows that (3,4,1,1) is counted under a(9). The a(1) = 1 through a(9) = 9 compositions:   1   11   12    1111   113     132      1114      1133       1143            21           122     231      1222      3311       1332            111          221     111111   2221      11111111   2331                         311              4111                 3411                         11111            1111111              11115                                                               12222                                                               22221                                                               51111                                                               111111111 MATHEMATICA Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], Sort[Total/@Union[ReplaceList[#, {___, s__, ___}:>{s}]]]==Range[n]&]], {n, 0, 15}] CROSSREFS Cf. A000079, A002033, A103295, A126796, A143823, A169942, A325676, A325677, A325683, A325684. Sequence in context: A143865 A071168 A091926 * A109606 A318727 A307806 Adjacent sequences:  A325682 A325683 A325684 * A325686 A325687 A325688 KEYWORD nonn,more AUTHOR Gus Wiseman, May 13 2019 STATUS approved

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Last modified April 5 12:34 EDT 2020. Contains 333241 sequences. (Running on oeis4.)