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 A325676 Number of compositions of n such that every distinct consecutive subsequence has a different sum. 34
 1, 1, 2, 4, 5, 10, 12, 24, 26, 47, 50, 96, 104, 172, 188, 322, 335, 552, 590, 938, 1002 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A composition of n is a finite sequence of positive integers summing to n. Compare to the definition of knapsack partitions (A108917). LINKS EXAMPLE The distinct consecutive subsequences of (1,4,4,3) together with their sums are:    1: {1}    3: {3}    4: {4}    5: {1,4}    7: {4,3}    8: {4,4}    9: {1,4,4}   11: {4,4,3}   12: {1,4,4,3} Because the sums are all different, (1,4,4,3) is counted under a(12). The a(1) = 1 through a(6) = 12 compositions:   (1)  (2)   (3)    (4)     (5)      (6)        (11)  (12)   (13)    (14)     (15)              (21)   (22)    (23)     (24)              (111)  (31)    (32)     (33)                     (1111)  (41)     (42)                             (113)    (51)                             (122)    (114)                             (221)    (132)                             (311)    (222)                             (11111)  (231)                                      (411)                                      (111111) MATHEMATICA Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], UnsameQ@@Total/@Union[ReplaceList[#, {___, s__, ___}:>{s}]]&]], {n, 0, 15}] CROSSREFS Cf. A000079, A103295, A108917, A169942, A235998, A321143. Cf. A325466, A325545, A325680, A325682, A325685, A325687, A325688. Sequence in context: A133732 A328221 A128215 * A097132 A321683 A321682 Adjacent sequences:  A325673 A325674 A325675 * A325677 A325678 A325679 KEYWORD nonn,more AUTHOR Gus Wiseman, May 13 2019 STATUS approved

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Last modified June 4 03:40 EDT 2020. Contains 334815 sequences. (Running on oeis4.)